Thursday, March 21, 2013

1103.0951 (Ikuo Satake et al.)

Gromov--Witten invariants for mirror orbifolds of simple elliptic

Ikuo Satake, Atsushi Takahashi
We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov--Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
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