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Holomorphic anomaly equations for the Hilbert schemes of points of K3 surfaces

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If you have a question about this talk, please contact Dhruv Ranganathan.

The generating series of Gromov-Witten invariants of the Hilbert scheme of points of a K3 surface are conjectured to be quasi-Jacobi forms and satisfy a holomorphic anomaly equation, which recursively determine the dependence on the non-modular part. I will sketch how one proves this conjecture for a meaningful part of the theory (genus 0 up to three markings). In the second part of this talk I will give an application to a conjectural Yau-Zaslow type formula for counts of genus 2 curves on HK 4 -folds of K32 type. The last part is joint work with Cao and Toda.

This talk is part of the Algebraic Geometry Seminar series.

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