Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(3): 573-591

Online first article May 7, 2021      Printed May 31, 2021

https://doi.org/10.4134/BKMS.b200236

Copyright © The Korean Mathematical Society.

Polynomiality of the equivariant Gromov-Witten theory of $\mathbb P^{r-1}$

Hyenho Lho

Chungnam National University

Abstract

We study the equivariant Gromov-Witten theory of $\PP^{r-1}$ for all $r\ge 2$. We prove a polynomiality property in $r$ of the Gromov-Witten classes of $\PP^{r-1}$. Using this polynomiality property, we define a set of polynomial valued classes in $H^*(\overline{M}_{g,n})$ which generalize the limit of Witten's $s$-spin classes studied by Pandharipande, Pixton and Zvonkine.

Keywords: Gromov-Witten theory, tautological class

MSC numbers: 14D23

Supported by: This work was supported by research fund of Chungnam National University.

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