Virasoro constraints for moduli of weighted pointed stable curves

TL;DR

This paper establishes Virasoro constraints for intersection numbers on Hassett's moduli spaces of weighted pointed curves, linking them to the KdV integrable hierarchy, thus advancing the understanding of their algebraic structure.

Contribution

It introduces Virasoro constraints for weighted pointed stable curves and demonstrates their connection to the KdV hierarchy, a novel extension in the field.

Findings

Virasoro constraints are formulated for Hassett's moduli spaces.

The constraints are shown to be governed by the KdV integrable hierarchy.

This work extends the algebraic understanding of intersection numbers on weighted curves.

Abstract

We formulate Virasoro constraints for the generating functions of the intersection numbers on Hassett's moduli of weighted pointed curves and show that they are governed by the KdV integrable hierarchy.