Cambridge Journal of Mathematics

Volume 7 (2019)

Number 3

Mixed-$\textrm{Spin-P}$ fields of Fermat polynomials

Pages: 319 – 364

DOI: https://dx.doi.org/10.4310/CJM.2019.v7.n3.a3

Authors

Huai-Liang Chang (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong)

Jun Li (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China)

Wei-Ping Li (Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong)

Melissa Chiu-Chu Liu (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Abstract

This is the first part of the project toward an effective algorithm to evaluate all genera Gromov–Witten invariants of quintic Calabi–Yau threefolds. In this paper, we introduce the notion of Mixed-$\textrm{Spin-P}$ fields, construct their moduli spaces, and construct the virtual cycles of these moduli spaces.

2010 Mathematics Subject Classification

14N35

Full Text (PDF format)

The first author was partially supported by Hong Kong GRF600711, GRF16301515 and GRF16301717.

The second author was partially supported by NSF grant DMS-1564500 and DMS-1601211.

The third author was partially supported by Hong Kong GRF602512, GRF16301515 and 16303518.

The fourth author was partially supported by NSF grant DMS-1206667, DMS-1159416 and DMS-1564497.

Received 12 November 2018

Published 11 September 2019