Maps, sheaves, and K3 surfaces

Details Maps, sheaves, and K3 surfaces Maps, sheaves, and K3 surfaces

2008-08-02

arxiv.org/abs/0808.0253v1

Mathematics

Algebraic Geometry

28 pages

Scientific paper

The conjectural equivalence of curve counting on Calabi-Yau 3-folds via stable maps and stable pairs is discussed. By considering Calabi-Yau 3-folds with K3 fibrations, the correspondence naturally connects curve and sheaf counting on K3 surfaces. New results and conjectures (with D. Maulik) about descendent integration on K3 surfaces are announced. The recent proof of the Yau-Zaslow conjecture is surveyed. The paper accompanies my lecture at the Clay research conference in Cambridge, MA in May 2008.

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