Basepoint free cycles on $\overline{M}_{0,n}$ from Gromov-Witten theory

TL;DR

This paper explores basepoint free cycles on the moduli space of stable rational curves using Gromov-Witten invariants of homogeneous spaces, providing explicit formulas and connections to conformal blocks divisors.

Contribution

It introduces a method to construct basepoint free cycles on ar{M}_{0,n} from Gromov-Witten theory and relates these to known divisors like conformal blocks.

Findings

Explicit intersection formulas for classes are derived.

Divisors for projective space are shown to be equivalent to conformal blocks divisors.

Constructs maps from ar{M}_{0,n} to GIT quotients using these cycles.

Abstract

Basepoint free cycles on the moduli space $\overline{M}_{0,n}$ of stable n-pointed rational curves, defined using Gromov-Witten invariants of smooth projective homogeneous spaces X are studied. Intersection formulas to find classes are given, with explicit examples for X a projective space, and X a smooth projective quadric hypersurface. When X is projective space, divisors are shown equivalent to conformal blocks divisors for type A at level one, giving maps from $\overline{M}_{0,n}$ to birational models constructed as GIT quotients, parametrizing configurations of weighted points supported on (generalized) Veronese curves.