Gromov-Witten invariants in family and Quantum cohomology

Article Type

Research Article

Publication Title

Manuscripta Mathematica

Abstract

A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r general lines while passing through given s general points, where r+2s=3d+2, firstly proved by R. Mukherjee, R. Kumar Singh and the fourth named author.

DOI

10.1007/s00229-025-01648-5

Publication Date

8-1-2025

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