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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von A. Takahashi (Osaka, JAP)

GW invariants for weighted projective lines mirror dual to simple elliptic singularities

We give isomophisms among three constructions of Frobenius (K. Saito's flat) structures for weighted projective lines mirror dual to simple elliptic singularities. In particular, we can show that the Fourier coefficients of the eta product η(3τ)3/η(τ), known to be all positive integers, are Gromov-Witten invariants and hence have a geometric meaning.