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Linear series with an đ-fold point on a general curve
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| Zeitschriftentitel: | Transactions of the American Mathematical Society |
|---|---|
| Personen und Körperschaften: | |
| In: | Transactions of the American Mathematical Society, 327, 1991, 1, S. 117-124 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
American Mathematical Society (AMS)
|
| Schlagwörter: |
| author_facet |
Schubert, David Schubert, David |
|---|---|
| author |
Schubert, David |
| spellingShingle |
Schubert, David Transactions of the American Mathematical Society Linear series with an đ-fold point on a general curve Applied Mathematics General Mathematics |
| author_sort |
schubert, david |
| spelling |
Schubert, David 0002-9947 1088-6850 American Mathematical Society (AMS) Applied Mathematics General Mathematics http://dx.doi.org/10.1090/s0002-9947-1991-1005937-x <p>A linear series <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper V comma script upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(V,\mathcal {L})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a curve <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point along a divisor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="dimension left-parenthesis upper V intersection upper H Superscript 0 Baseline left-parenthesis upper X comma script upper L left-parenthesis negative upper D right-parenthesis right-parenthesis right-parenthesis greater-than-or-equal-to dimension upper V minus 1"> <mml:semantics> <mml:mrow> <mml:mi>dim</mml:mi> <mml:mo>âĄ<!-- ⥠--></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>â©<!-- â© --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> <mml:mspace width="thickmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mo>â<!-- â --></mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>â„<!-- â„ --></mml:mo> <mml:mi>dim</mml:mi> <mml:mspace width="thickmathspace" /> <mml:mi>V</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\dim (V \cap {H^0}\;(X,\mathcal {L}\,(- D))) \geq \dim \;V - 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The dimensions of the families of linear series with an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point are determined for general curves.</p> Linear series with an đ-fold point on a general curve Transactions of the American Mathematical Society |
| doi_str_mv |
10.1090/s0002-9947-1991-1005937-x |
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Online Free |
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Mathematik |
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ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9zMDAwMi05OTQ3LTE5OTEtMTAwNTkzNy14 |
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DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 DE-L229 DE-D275 DE-Bn3 DE-Brt1 DE-Zwi2 DE-D161 DE-Gla1 DE-Zi4 DE-15 |
| imprint |
American Mathematical Society (AMS), 1991 |
| imprint_str_mv |
American Mathematical Society (AMS), 1991 |
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0002-9947 1088-6850 |
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0002-9947 1088-6850 |
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English |
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American Mathematical Society (AMS) (CrossRef) |
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schubert1991linearserieswithanpoegfoldpointonageneralcurve |
| publishDateSort |
1991 |
| publisher |
American Mathematical Society (AMS) |
| recordtype |
ai |
| record_format |
ai |
| series |
Transactions of the American Mathematical Society |
| source_id |
49 |
| title |
Linear series with an đ-fold point on a general curve |
| title_unstemmed |
Linear series with an đ-fold point on a general curve |
| title_full |
Linear series with an đ-fold point on a general curve |
| title_fullStr |
Linear series with an đ-fold point on a general curve |
| title_full_unstemmed |
Linear series with an đ-fold point on a general curve |
| title_short |
Linear series with an đ-fold point on a general curve |
| title_sort |
linear series with an đ-fold point on a general curve |
| topic |
Applied Mathematics General Mathematics |
| url |
http://dx.doi.org/10.1090/s0002-9947-1991-1005937-x |
| publishDate |
1991 |
| physical |
117-124 |
| description |
<p>A linear series <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper V comma script upper L right-parenthesis">
<mml:semantics>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>V</mml:mi>
<mml:mo>,</mml:mo>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:annotation encoding="application/x-tex">(V,\mathcal {L})</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> on a curve <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X">
<mml:semantics>
<mml:mi>X</mml:mi>
<mml:annotation encoding="application/x-tex">X</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> has an <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N">
<mml:semantics>
<mml:mi>N</mml:mi>
<mml:annotation encoding="application/x-tex">N</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-fold point along a divisor <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D">
<mml:semantics>
<mml:mi>D</mml:mi>
<mml:annotation encoding="application/x-tex">D</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> of degree <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N">
<mml:semantics>
<mml:mi>N</mml:mi>
<mml:annotation encoding="application/x-tex">N</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula> if <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="dimension left-parenthesis upper V intersection upper H Superscript 0 Baseline left-parenthesis upper X comma script upper L left-parenthesis negative upper D right-parenthesis right-parenthesis right-parenthesis greater-than-or-equal-to dimension upper V minus 1">
<mml:semantics>
<mml:mrow>
<mml:mi>dim</mml:mi>
<mml:mo>âĄ<!-- ⥠--></mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>V</mml:mi>
<mml:mo>â©<!-- â© --></mml:mo>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mn>0</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mspace width="thickmathspace" />
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>X</mml:mi>
<mml:mo>,</mml:mo>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi>
</mml:mrow>
<mml:mspace width="thinmathspace" />
<mml:mo stretchy="false">(</mml:mo>
<mml:mo>â<!-- â --></mml:mo>
<mml:mi>D</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>â„<!-- â„ --></mml:mo>
<mml:mi>dim</mml:mi>
<mml:mspace width="thickmathspace" />
<mml:mi>V</mml:mi>
<mml:mo>â<!-- â --></mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:annotation encoding="application/x-tex">\dim (V \cap {H^0}\;(X,\mathcal {L}\,(- D))) \geq \dim \;V - 1</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>. The dimensions of the families of linear series with an <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N">
<mml:semantics>
<mml:mi>N</mml:mi>
<mml:annotation encoding="application/x-tex">N</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-fold point are determined for general curves.</p> |
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| description | <p>A linear series <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper V comma script upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(V,\mathcal {L})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a curve <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point along a divisor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="dimension left-parenthesis upper V intersection upper H Superscript 0 Baseline left-parenthesis upper X comma script upper L left-parenthesis negative upper D right-parenthesis right-parenthesis right-parenthesis greater-than-or-equal-to dimension upper V minus 1"> <mml:semantics> <mml:mrow> <mml:mi>dim</mml:mi> <mml:mo>âĄ<!-- ⥠--></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>â©<!-- â© --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> <mml:mspace width="thickmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mo>â<!-- â --></mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>â„<!-- â„ --></mml:mo> <mml:mi>dim</mml:mi> <mml:mspace width="thickmathspace" /> <mml:mi>V</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\dim (V \cap {H^0}\;(X,\mathcal {L}\,(- D))) \geq \dim \;V - 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The dimensions of the families of linear series with an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point are determined for general curves.</p> |
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| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTA5MC9zMDAwMi05OTQ3LTE5OTEtMTAwNTkzNy14 |
| imprint | American Mathematical Society (AMS), 1991 |
| imprint_str_mv | American Mathematical Society (AMS), 1991 |
| institution | DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15 |
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| physical | 117-124 |
| publishDate | 1991 |
| publishDateSort | 1991 |
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| series | Transactions of the American Mathematical Society |
| source_id | 49 |
| spelling | Schubert, David 0002-9947 1088-6850 American Mathematical Society (AMS) Applied Mathematics General Mathematics http://dx.doi.org/10.1090/s0002-9947-1991-1005937-x <p>A linear series <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper V comma script upper L right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(V,\mathcal {L})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a curve <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point along a divisor <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="dimension left-parenthesis upper V intersection upper H Superscript 0 Baseline left-parenthesis upper X comma script upper L left-parenthesis negative upper D right-parenthesis right-parenthesis right-parenthesis greater-than-or-equal-to dimension upper V minus 1"> <mml:semantics> <mml:mrow> <mml:mi>dim</mml:mi> <mml:mo>âĄ<!-- ⥠--></mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>â©<!-- â© --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msup> </mml:mrow> <mml:mspace width="thickmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">(</mml:mo> <mml:mo>â<!-- â --></mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>â„<!-- â„ --></mml:mo> <mml:mi>dim</mml:mi> <mml:mspace width="thickmathspace" /> <mml:mi>V</mml:mi> <mml:mo>â<!-- â --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\dim (V \cap {H^0}\;(X,\mathcal {L}\,(- D))) \geq \dim \;V - 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The dimensions of the families of linear series with an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper N"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding="application/x-tex">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-fold point are determined for general curves.</p> Linear series with an đ-fold point on a general curve Transactions of the American Mathematical Society |
| spellingShingle | Schubert, David, Transactions of the American Mathematical Society, Linear series with an đ-fold point on a general curve, Applied Mathematics, General Mathematics |
| title | Linear series with an đ-fold point on a general curve |
| title_full | Linear series with an đ-fold point on a general curve |
| title_fullStr | Linear series with an đ-fold point on a general curve |
| title_full_unstemmed | Linear series with an đ-fold point on a general curve |
| title_short | Linear series with an đ-fold point on a general curve |
| title_sort | linear series with an đ-fold point on a general curve |
| title_unstemmed | Linear series with an đ-fold point on a general curve |
| topic | Applied Mathematics, General Mathematics |
| url | http://dx.doi.org/10.1090/s0002-9947-1991-1005937-x |