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A note on Virasoro constraints for products

Hsian-Hua Tseng

Abstract

We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.

A note on Virasoro constraints for products

Abstract

We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.
Paper Structure (11 sections, 2 theorems, 49 equations)

This paper contains 11 sections, 2 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Acknowledgment
  3. Preliminary materials
  4. Cohomological field theory
  5. The $R$-matrix action
  6. Givental-Teleman classification
  7. Product targets
  8. The Gromov-Witten CohFT
  9. CohFT of a product
  10. Virasoro constraints
  11. Proof of Theorem \ref{['thm:main']}

Key Result

Theorem 1.2

Suppose the quantum cohomology of $Y$ is semi-simple at some point. Then Virasoro constraints for $X\times Y$ hold if and only if Virasoro constraints hold for $X$.

Theorems & Definitions (3)

  • Theorem 1.2
  • Theorem 2.1
  • Remark 3.5