Lower bounds for enumerative counts of positive-genus real curves

Jingchen Niu; Aleksey Zinger

doi:10.1016/j.aim.2018.09.024

Lower bounds for enumerative counts of positive-genus real curves

Jingchen Niu
, Aleksey Zinger

Mathematics

Stony Brook University
University of Arizona

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

3 Scopus citations

Abstract

We transform the positive-genus real Gromov–Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for Hodge integrals.

Original language	English
Pages (from-to)	191-247
Number of pages	57
Journal	Advances in Mathematics
Volume	339
DOIs	https://doi.org/10.1016/j.aim.2018.09.024
State	Published - Dec 1 2018

Keywords

Enumerative geometry
Hodge integrals
Real Gromov–Witten theory

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10.1016/j.aim.2018.09.024

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title = "Lower bounds for enumerative counts of positive-genus real curves",

abstract = "We transform the positive-genus real Gromov–Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for Hodge integrals.",

keywords = "Enumerative geometry, Hodge integrals, Real Gromov–Witten theory",

author = "Jingchen Niu and Aleksey Zinger",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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day = "1",

doi = "10.1016/j.aim.2018.09.024",

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T1 - Lower bounds for enumerative counts of positive-genus real curves

AU - Niu, Jingchen

AU - Zinger, Aleksey

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We transform the positive-genus real Gromov–Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for Hodge integrals.

AB - We transform the positive-genus real Gromov–Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for Hodge integrals.

KW - Enumerative geometry

KW - Hodge integrals

KW - Real Gromov–Witten theory

UR - https://www.scopus.com/pages/publications/85053890332

U2 - 10.1016/j.aim.2018.09.024

DO - 10.1016/j.aim.2018.09.024

M3 - Article

AN - SCOPUS:85053890332

SN - 0001-8708

VL - 339

SP - 191

EP - 247

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Lower bounds for enumerative counts of positive-genus real curves

Abstract

Keywords

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