Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Orbifold quantum cohomology of weighted projective spaces


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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    References


    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