Higher genus relative and orbifold Gromov–Witteninvariants
Hsian-Hua Tseng, Fenglong You
Abstract
Given a smooth projective variety [math] and a smooth divisor [math] , we study relative Gromov–Witten invariants of [math] and the corresponding orbifold Gromov–Witten invariants of the [math] root stack [math] . For sufficiently large [math] , we prove that orbifold Gromov–Witten invariants of [math] are polynomials in [math] . Moreover, higher-genus relative Gromov–Witten invariants of [math] are exactly the constant terms of the corresponding higher-genus orbifold Gromov–Witten invariants of [math] . We also provide a new proof for the equality between genus-zero relative and orbifold Gromov–Witten invariants, originally proved by Abramovich, Cadman and Wise (2017). When [math] is sufficiently large and [math] is a curve, we prove that stationary relative invariants of [math] are equal to the stationary orbifold invariants in all genera.