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Convergence of quantum cohomology by quantum Lefschetz

✍ Scribed by Iritani, Hiroshi

Book ID
118740404
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2007
Tongue
English
Weight
434 KB
Volume
2007
Category
Article
ISSN
0075-4102

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✦ Synopsis

Quantum Lefschetz theorem by Coates and Givental [4] 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 semisimplicity and the Virasoro conjecture for the Gromov-Witten theories of (not necessarily Fano) projective toric manifolds.

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