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Hyper-Kaehler varieties and Jacobi forms

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Georg Oberdieck (MIT) - Seminar Algebraic Geometry (SAG)

  • Seminar
When Nov 16, 2017
from 10:30 am to 11:30 am
Where Bonn, Hörsaal MPI, Vivatsgasse 7, 53111 Bonn
Contact Name Sachinidis
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The Yau-Zaslow formula relates the number of rational curves on a K3 surface to Fourier coefficients of the modular discriminant. Hyper-Kaehler varieties are analogs of K3 surfaces in higher dimension, and an analog of rational curves are the uniruled divisors. I will discuss how one can use Gromov-Witten theory to enumerate these divisors in terms of Jacobi forms. More generally, the full Gromov-Witten theory of hyper-Kaehler varieties is conjecturally governed by Jacobi forms. I will explain how holomorphic anomaly equations fit into this picture.