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
Recommended Citation
Biswas, Indranil; Das, Nilkantha; Oh, Jeongseok; and Paul, Anantadulal, "Gromov-Witten invariants in family and Quantum cohomology" (2025). Journal Articles. 5399.
https://digitalcommons.isical.ac.in/journal-articles/5399