Maps, sheaves, and K3 surfaces
Algebraic Geometry
2008-08-05 v1 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.0808.0253,
title = {Maps, sheaves, and K3 surfaces},
author = {R. Pandharipande},
journal= {arXiv preprint arXiv:0808.0253},
year = {2008}
}
Comments
28 pages