Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds
An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invar...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Sprache: | English |
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Інститут математики НАН України
2017
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| Zitieren: | Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds / Chiu-Chu Melissa Liu, A. Sheshmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 29 назв. — англ. |
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Liu, Chiu-Chu Melissa Sheshmani, A. 2019-02-18T15:36:56Z 2019-02-18T15:36:56Z 2017 Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds / Chiu-Chu Melissa Liu, A. Sheshmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 29 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14C05; 14D20; 14F05; 14J30; 14N10 DOI:10.3842/SIGMA.2017.048 https://nasplib.isofts.kiev.ua/handle/123456789/148556 An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold. The first author would like to thank Tom Graber for his suggestion of generalizing the computations for toric manifolds in [23] to GKM manifolds. The second author would like to thank the Columbia University for hospitality during his visits. We wish to thank Rahul Pandharipande for his comments on an earlier version of this paper. This work is partially supported by NSF DMS-1159416 and NSF DMS-1206667. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds |
| spellingShingle |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds Liu, Chiu-Chu Melissa Sheshmani, A. |
| title_short |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds |
| title_full |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds |
| title_fullStr |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds |
| title_full_unstemmed |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds |
| title_sort |
equivariant gromov-witten invariants of algebraic gkm manifolds |
| author |
Liu, Chiu-Chu Melissa Sheshmani, A. |
| author_facet |
Liu, Chiu-Chu Melissa Sheshmani, A. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148556 |
| citation_txt |
Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds / Chiu-Chu Melissa Liu, A. Sheshmani // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 29 назв. — англ. |
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AT liuchiuchumelissa equivariantgromovwitteninvariantsofalgebraicgkmmanifolds AT sheshmania equivariantgromovwitteninvariantsofalgebraicgkmmanifolds |
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2025-12-07T20:55:37Z |
| last_indexed |
2025-12-07T20:55:37Z |
| _version_ |
1850884423603453952 |