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MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY
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| Zeitschriftentitel: | Forum of Mathematics, Sigma |
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| Personen und Körperschaften: | , , , |
| In: | Forum of Mathematics, Sigma, 4, 2016 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
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| Schlagwörter: |
| author_facet |
CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV |
|---|---|
| author |
CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV |
| spellingShingle |
CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV Forum of Mathematics, Sigma MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY Computational Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematical Physics Statistics and Probability Algebra and Number Theory Theoretical Computer Science Analysis |
| author_sort |
cavalieri, renzo |
| spelling |
CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV 2050-5094 Cambridge University Press (CUP) Computational Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematical Physics Statistics and Probability Algebra and Number Theory Theoretical Computer Science Analysis http://dx.doi.org/10.1017/fms.2016.7 <jats:p>We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline1" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> of weights, the moduli space of tropical <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline2" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula>-stable curves can be given the structure of a balanced fan if and only if <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline3" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.</jats:p> MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY Forum of Mathematics, Sigma |
| doi_str_mv |
10.1017/fms.2016.7 |
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Online Free |
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Mathematik Informatik Physik |
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Cambridge University Press (CUP), 2016 |
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Cambridge University Press (CUP), 2016 |
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2050-5094 |
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| title |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_unstemmed |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_full |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_fullStr |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_full_unstemmed |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_short |
MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_sort |
moduli spaces of rational weighted stable curves and tropical geometry |
| topic |
Computational Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematical Physics Statistics and Probability Algebra and Number Theory Theoretical Computer Science Analysis |
| url |
http://dx.doi.org/10.1017/fms.2016.7 |
| publishDate |
2016 |
| physical |
|
| description |
<jats:p>We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline1" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> of weights, the moduli space of tropical <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline2" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula>-stable curves can be given the structure of a balanced fan if and only if <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline3" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.</jats:p> |
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| author | CAVALIERI, RENZO, HAMPE, SIMON, MARKWIG, HANNAH, RANGANATHAN, DHRUV |
| author_facet | CAVALIERI, RENZO, HAMPE, SIMON, MARKWIG, HANNAH, RANGANATHAN, DHRUV, CAVALIERI, RENZO, HAMPE, SIMON, MARKWIG, HANNAH, RANGANATHAN, DHRUV |
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| description | <jats:p>We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline1" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> of weights, the moduli space of tropical <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline2" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula>-stable curves can be given the structure of a balanced fan if and only if <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline3" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.</jats:p> |
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| institution | DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229 |
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| spelling | CAVALIERI, RENZO HAMPE, SIMON MARKWIG, HANNAH RANGANATHAN, DHRUV 2050-5094 Cambridge University Press (CUP) Computational Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Mathematical Physics Statistics and Probability Algebra and Number Theory Theoretical Computer Science Analysis http://dx.doi.org/10.1017/fms.2016.7 <jats:p>We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline1" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> of weights, the moduli space of tropical <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline2" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula>-stable curves can be given the structure of a balanced fan if and only if <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S2050509416000074_inline3" /><jats:tex-math>$w$</jats:tex-math></jats:alternatives></jats:inline-formula> has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.</jats:p> MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY Forum of Mathematics, Sigma |
| spellingShingle | CAVALIERI, RENZO, HAMPE, SIMON, MARKWIG, HANNAH, RANGANATHAN, DHRUV, Forum of Mathematics, Sigma, MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY, Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis |
| title | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_full | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_fullStr | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_full_unstemmed | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_short | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| title_sort | moduli spaces of rational weighted stable curves and tropical geometry |
| title_unstemmed | MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY |
| topic | Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis |
| url | http://dx.doi.org/10.1017/fms.2016.7 |