Moduli of weighted stable maps and their gravitational descendants

TL;DR

This paper investigates the intersection theory on moduli spaces of weighted stable maps, providing formulas for how gravitational descendants change under wall crossings and relating weighted and usual descendants.

Contribution

It introduces a detailed structure of weighted stable map moduli spaces and derives formulas linking weighted and usual gravitational descendants.

Findings

Derived formulas for descendant changes under wall crossing.

Expressed weighted descendants in terms of usual ones.

Provided structural insights into weighted stable map moduli spaces.

Abstract

We study the intersection theory on the moduli spaces of maps of $n$-pointed curves $f:(C,s_1,... s_n)\to V$ which are stable with respect to a weight data $(a_1,..., a_n)$, $0\le a_i\le 1$. After describing the structure of these moduli spaces, we prove a formula describing the way each descendant changes under a wall crossing. As a corollary, we compute the weighted descendants in terms of the usual ones, i.e. for the weight data $(1,...,1)$, and vice versa.