Genus-1 Virasoro conjecture along quantum volume direction

TL;DR

This paper proves that the genus-1 Virasoro conjecture for Gromov-Witten invariants remains valid when differentiated along the quantum volume element for all smooth projective varieties, supporting the conjecture's validity.

Contribution

It establishes the derivative of the genus-1 Virasoro conjecture along the quantum volume direction for all smooth projective varieties, providing new evidence for the conjecture.

Findings

Derivative of genus-1 Virasoro conjecture holds along quantum volume direction

Supports the validity of the Virasoro conjecture for all smooth projective varieties

Provides new evidence for the conjecture's universality

Abstract

In this paper, we show that the derivative of the genus-1 Virasoro conjecture for Gromov-Witten invariants along the direction of quantum volume element holds for all smooth projective varieties. This result provides new evidence for the Virasoro conjecture.