Mirror Symmetry and New "Quantum" Invariants for Quasi-homogeneous Singularities
New Developments in the Geometry and Physics of Gromov-Witten Theory
May 23, 2006 11:00 AM to 12:00 PM
Speakers:
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Abstract: |
I will describe joint work in progress with Huijun Fan and Yongbin Ruan in which we construct, for every non-degenerate quasi-homogeneous singularity, a moduli space of decorated stable curves and a virtual cycle on that space. Moreover, for each automorphism of the singularity, we associate a ring--the Milnor ring of the singularity restricted to the fixed locus of the automorphism. The virtual cycle can be used to put a new ring structure on the direct sum of these to form a Frobenius algebra.
In all the cases computed so far, the Frobenius algebra associated to the singularity is "mirror dual" to the orbifold Milnor ring (or orbifold Landau-Ginzburg B-model) described by Kaufmann and Intriligator-Vafa. In the special case of the A_n singularity, our constructions give a refinement of the theory of higher spin curves. |
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