Refined Descendant Invariants of Toric Surfaces

Lev Blechman; Eugenii Shustin

doi:10.1007/s00454-019-00093-y

Refined Descendant Invariants of Toric Surfaces

Lev Blechman, Eugenii Shustin

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We construct refined tropical enumerative genus zero invariants of toric surfaces that specialize to the tropical descendant genus zero invariants introduced by Markwig and Rau when the quantum parameter tends to 1. In the case of trivalent tropical curves our invariants turn to be the Göttsche–Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig–Rau descendant invariants that generalizes the Göttsche–Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.

Original language	English
Pages (from-to)	180-208
Number of pages	29
Journal	Discrete and Computational Geometry
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s00454-019-00093-y
State	Published - 15 Jul 2019

Keywords

Gromov–Witten invariants
Moduli spaces of tropical curves
Tropical curves
Tropical descendant invariants
Tropical enumerative geometry

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-019-00093-y

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title = "Refined Descendant Invariants of Toric Surfaces",

abstract = "We construct refined tropical enumerative genus zero invariants of toric surfaces that specialize to the tropical descendant genus zero invariants introduced by Markwig and Rau when the quantum parameter tends to 1. In the case of trivalent tropical curves our invariants turn to be the G{\"o}ttsche–Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig–Rau descendant invariants that generalizes the G{\"o}ttsche–Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.",

keywords = "Gromov–Witten invariants, Moduli spaces of tropical curves, Tropical curves, Tropical descendant invariants, Tropical enumerative geometry",

author = "Lev Blechman and Eugenii Shustin",

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AU - Shustin, Eugenii

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N2 - We construct refined tropical enumerative genus zero invariants of toric surfaces that specialize to the tropical descendant genus zero invariants introduced by Markwig and Rau when the quantum parameter tends to 1. In the case of trivalent tropical curves our invariants turn to be the Göttsche–Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig–Rau descendant invariants that generalizes the Göttsche–Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.

AB - We construct refined tropical enumerative genus zero invariants of toric surfaces that specialize to the tropical descendant genus zero invariants introduced by Markwig and Rau when the quantum parameter tends to 1. In the case of trivalent tropical curves our invariants turn to be the Göttsche–Schroeter refined broccoli invariants. We show that this is the only possible refinement of the Markwig–Rau descendant invariants that generalizes the Göttsche–Schroeter refined broccoli invariants. We discuss also the computational aspect (a lattice path algorithm) and exhibit some examples.

KW - Gromov–Witten invariants

KW - Moduli spaces of tropical curves

KW - Tropical curves

KW - Tropical descendant invariants

KW - Tropical enumerative geometry

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U2 - 10.1007/s00454-019-00093-y

DO - 10.1007/s00454-019-00093-y

M3 - مقالة

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VL - 62

SP - 180

EP - 208

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 1

ER -

Refined Descendant Invariants of Toric Surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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