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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 |
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| 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)
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| Schlagwörter: |
| Zusammenfassung: | <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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| Umfang: | 117-124 |
| ISSN: |
0002-9947
1088-6850 |
| DOI: | 10.1090/s0002-9947-1991-1005937-x |