Convergence of quantum cohomology by quantum Lefschetz
Abstract
Description
Quantum Lefschetz theorem by Coates and Givental gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the genus 0 theory for original X converges. As a byproduct, we prove the semi-simplicity and the Virasoro conjecture for the Gromov-Witten theories of (not necessarily Fano) projective toric manifolds.
35pages; v2 minor changes, v3 changes in exposition in Introduction and section 3, added Corollary 6.9, v4 changes in exposition in section3, changes in notation: fundamental solution L is replaced with its inverse
35pages; v2 minor changes, v3 changes in exposition in Introduction and section 3, added Corollary 6.9, v4 changes in exposition in section3, changes in notation: fundamental solution L is replaced with its inverse