Orbifold quantum cohomology of weighted projective spaces

Mann, Etienne

doi:10.1090/S1056-3911-07-00465-1

Author: Etienne Mann
Journal: J. Algebraic Geom. 17 (2008), 137-166
DOI: https://doi.org/10.1090/S1056-3911-07-00465-1
Published electronically: August 16, 2007
MathSciNet review: 2357682
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Abstract | References | Additional Information

Abstract:

In this article, we prove the following results.

We show a mirror theorem: the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective spaces is isomorphic to the one attached to a specific Laurent polynomial.

We show a reconstruction theorem; that is, we can reconstruct in an algorithmic way the full genus $0$ Gromov-Witten potential from the $3$-point invariants.

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Additional Information

Etienne Mann
Affiliation: SISSA, via Beirut 2-4, I-34014 Trieste, Italy
Address at time of publication: Département de Mathématiques, Université de Montpellier 2, CC 5149, Place Eugène Bataillon, F-34 095 Montpellier Cedex 5, France
Email: etienne.mann@gmail.com

Received by editor(s): December 9, 2005
Received by editor(s) in revised form: August 31, 2006
Published electronically: August 16, 2007