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arXiv · 2408.06616

Gromov-Witten invariants in family and quantum cohomology

Indranil Biswas·Nilkantha Das·Jeongseok Oh·Anantadulal Paul
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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.

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Indranil Biswas, Nilkantha Das, Jeongseok Oh, Anantadulal Paul. 2025-06-09. Gromov-Witten invariants in family and quantum cohomology. https://arxiv.org/abs/2408.06616

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