Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities

Details Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities

2011-03-04

arxiv.org/abs/1103.0951v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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 an 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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