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


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.


Download Citation

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


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

Primary: 53D45
Secondary: 14N35

Rights: Copyright © 2021 by Kyoto University


Vol.61 • No. 2 • June 2021
Back to Top