Relative and orbifold Gromov-Witten invariants

TL;DR

This paper establishes a correspondence between genus zero Gromov-Witten invariants of smooth schemes relative to divisors and orbifold Gromov-Witten invariants of associated root stacks, unifying two approaches in enumerative geometry.

Contribution

It proves that relative Gromov-Witten invariants are equivalent to orbifold Gromov-Witten invariants for certain root stacks, providing a new perspective and tools for computations.

Findings

Genus zero relative Gromov-Witten invariants match orbifold invariants of root stacks.

The result bridges relative and orbifold Gromov-Witten theories.

Provides a method to compute invariants via orbifold techniques.

Abstract

We prove that genus zero Gromov--Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus zero orbifold Gromov--Witten invariants of an appropriate root stack construction along the divisor.