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June 2021 WDVV-type relations for Welschinger invariants: Applications
Xujia Chen, Aleksey Zinger
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Kyoto J. Math. 61(2): 339-376 (June 2021). DOI: 10.1215/21562261-2021-0005

Abstract

We first recall Solomon’s relations for Welschinger invariants counting real curves in real symplectic fourfolds and the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV)-style relations for Welschinger invariants counting real curves in real symplectic sixfolds with some symmetry. We then explicitly demonstrate that, in some important cases (projective spaces with standard conjugations, real blowups of the projective plane, and two- and threefold products of the one-dimensional projective space with two involutions each), these relations provide complete recursions determining all Welschinger invariants from basic input. We include extensive tables of Welschinger invariants in low degrees obtained from these recursions with Mathematica. These invariants provide lower bounds for counts of real rational curves, including with curve insertions in smooth algebraic threefolds.

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Xujia Chen. Aleksey Zinger. "WDVV-type relations for Welschinger invariants: Applications." Kyoto J. Math. 61 (2) 339 - 376, June 2021. https://doi.org/10.1215/21562261-2021-0005

Information

Received: 4 September 2019; Revised: 5 August 2020; Accepted: 24 August 2020; Published: June 2021
First available in Project Euclid: 22 March 2021

Digital Object Identifier: 10.1215/21562261-2021-0005

Subjects:
Primary: 53D45
Secondary: 14N35

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 2 • June 2021
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