Structures in genus‐zero relative Gromov–Witten theory

Abstract

In this paper, we define genus‐zero relative Gromov–Witten invariants with negative contact orders. Using this, we construct relative quantum cohomology rings and Givental formalism. A version of Virasoro constraints also follows from it.

Mirror theorems for root stacks and relative pairs

“…That is, the ages are of the form i r, for r sufficiently large. In [18], the correspondence between genus-zero relative and orbifold invariants has been generalized to include orbifold invariants with large ages. The extra orbifold invariants correspond to relative invariants with negative contact orders as defined in [18].…”

“…In [18], the correspondence between genus-zero relative and orbifold invariants has been generalized to include orbifold invariants with large ages. The extra orbifold invariants correspond to relative invariants with negative contact orders as defined in [18]. Givental's formalism for genus-zero relative Gromov-Witten theory has also been worked out in [18].…”

“…The extra orbifold invariants correspond to relative invariants with negative contact orders as defined in [18]. Givental's formalism for genus-zero relative Gromov-Witten theory has also been worked out in [18].…”

“…In Section 4, we obtain a Givental style mirror theorem for relative Gromov-Witten invariants. That is, the I-function for relative Gromov-Witten invariants lies in Givental's Lagrangian cone for relative invariants, as defined in [18]. In particular, the result in [2] and [40] is already sufficient if one only considers the restricted J-function, defined in Section 4, where each invariant only contains one relative marking.…”

“…Genus-zero invariants of root stacks and genus-zero relative invariants are closely related. Following the formalism of [18], we rephrase our result as a mirror theorem of relative theory in this section.…”