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Abstract
Quantum Lefschetz theorem by Coates and Givental [T. Coates, A. B. Givental, Quantum Riemann-Roch, Lefschetz and Serre, math.AG/0110142.] 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.
Received: 2005-10-24
Revised: 2006-05-01
Published Online: 2007-12-07
Published in Print: 2007-09-26
© Walter de Gruyter
