Convergence of quantum cohomology by quantum Lefschetz

Details Convergence of quantum cohomology by quantum Lefschetz Convergence of quantum cohomology by quantum Lefschetz

2005-06-13

arxiv.org/abs/math/0506236v4

J. Reine Angew. Math. 610 (2007), pp.29--69

Mathematics

Differential Geometry

35pages; v2 minor changes, v3 changes in exposition in Introduction and section 3, added Corollary 6.9, v4 changes in expositi

Scientific paper

10.1515/CRELLE.2007

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.

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