Algebraic Geometry and Topological Strings Seminar 

04/11/2005, 12:00 — 13:00 — Amphitheatre Pa3, Mathematics Building
Emanuel Scheidegger, Institute for Theoretical Physics, TU Vienna

Topological String on K3 Fibrations

We explain that certain Gopakumar-Vafa invariants (and, conjecturally, hence Gromow-Witten invariants) for Calabi-Yau manifolds that admit a K3 fibration can be collected in a generating function. This function is in general an automorphic form determined by the fibration. In the class of K3 fibrations in toric varieties in which the Picard lattice of the fiber has rank one, we show how this automorphic form can be determined from the topology of the fibration.

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REFERENCES:

R. Gopakumar, C. Vafa, M-theory and topological strings,II, hep-th/9812127.
S. Katz, A. Klemm, C. Vafa, M-Theory, Topological Strings and Spinning Black Holes, hep-th/9910181.
J. Harvey, G. Moore, Algebras, BPS States, and Strings, hep-th/9510182.
M. Marino, G. Moore, Counting higher genus curves in a Calabi-Yau manifold, hep-th/9808131.
A. Klemm, M. Kreuzer, E. Riegler, E. Scheidegger, Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections, hep-th/0410018.
E. Scheidegger,Topological Strings on K3 fibrations, I, to appear.