Counting rational curves on \(K3\) surfaces
From MaRDI portal
Publication:1974899
DOI10.1215/S0012-7094-99-09704-1zbMATH Open0999.14018arXivalg-geom/9701019MaRDI QIDQ1974899
Author name not available (Why is that?)
Publication date: 27 March 2000
Published in: (Search for Journal in Brave)
Abstract: The aim of these notes is to explain the remarkable formula found by Yau and Zaslow to express the number of rational curves on a K3 surface. Projective K3 surfaces fall into countably many families F(g) (g>0); a surface in F(g) admits a g-dimensional linear system of curves of genus g. Such a system contains a positive number, say n(g), of rational (highly singular) curves. The formula is sum n(g) q^g = q/D((q), where D(q) = q prod (1-q^n)^{24} is the well-known modular form of weight 12.
Full work available at URL: https://arxiv.org/abs/alg-geom/9701019
No records found.
No records found.
This page was built for publication: Counting rational curves on \(K3\) surfaces
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1974899)
