Witten-Dijkgraaf-Verlinde-Verlinde equation and its application to relative Gromov-Witten theory

Abstract

We derive a recursive formula for certain relative Gromov-Witten invariants with a maximal tangency condition via the Witten-Dijkgraaf-Verlinde-Verlinde equation. For certain relative pairs, we get explicit formulae of invariants using the recursive formula.

Relative Gromov-Witten invariants and the enumerative meaning of mirror maps for toric Calabi-Yau orbifolds

“…It results in several structural properties for relative Gromov-Witten theory such as relative quantum cohomology ring, topological recursion relation (TRR), WDVV equation, Virasoro constraint (genus zero), Givental's formalism etc. An application of WDVV equation for relative Gromov-Witten theory has been worked out in [19]. In a forthcoming joint work with H. Fan and L. Wu [21], we will study structures of higher genus relative Gromov-Witten theory.…”