The enumerative geometry of K3 surfaces and modular forms
| dc.creator | Bryan, Jim | |
| dc.creator | Leung, Naichung Conan | |
| dc.date | 1997-11-24 | |
| dc.date.accessioned | 2026-07-07T01:51:20Z | |
| dc.date.available | 2026-07-07T01:51:20Z | |
| dc.description | We prove the conjectures of Yau-Zaslow and Gottsche concerning the number curves on K3 surfaces. Specifically, let X be a K3 surface and C be a holomorphic curve in X representing a primitive homology class. We count the number of curves of geometric genus g with n nodes passing through g generic points in X in the linear system |C| for any g and n satisfying C^2=2g+2n-2. When g=0, this coincides with the enumerative problem studied by Yau and Zaslow who obtained a conjectural generating function for the numbers. Recently, Gottsche has generalized their conjecture to arbitrary g in terms of quasi-modular forms. We prove these formulas using Gromov-Witten invariants for families, a degeneration argument, and an obstruction bundle computation. Our methods also apply to P^2 blown up at 9 points where we show that the ordinary Gromov-Witten invariants of genus g constrained to g points are also given in terms of quasi-modular forms. | |
| dc.description | 24 pages, LaTeX2e with eepic macros | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9711031 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9711031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/274 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | 14N10;14J28;53C57 | |
| dc.title | The enumerative geometry of K3 surfaces and modular forms | |
| dc.type | text |