Correspondences of K3 surface via moduli of sheaves

K3 表面通过滑轮模量的对应关系

• 批准号: EP/D061997/1
• 负责人: Viacheslav Nikulin
• 金额: $ 36.37万
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD061997%2F1
• 关键词: Correspondences; K3; surface; via; moduli

K3 surfaces is one of the most remarkable classes of algebraic surfaces which are very important in contemporary Mathematics and Physics. During last 40 years there was a big progress in their understanding, but we still discover some their new, unexpected and important properties. , elements of the Picard lattice (generated by algebraic curves) of a K3 surface deliver remarkable two-dimensional algebraic cycles on the product of the K3 surface with itself, and a correspondence of the K3 surface with itself. It happens when moduli of coherent sheaves over a K3 surface with a given Mukai vector coincide with this K3 surface. We want to study this phenomenon in details.

K3曲面是代数曲面中最引人注目的一类，在当代数学和物理学中占有重要地位。近40年来，人们对它们的认识有了很大的进步，但我们仍然发现了一些新的、意想不到的和重要的性质。， K3表面的皮卡德晶格元素（由代数曲线生成）在K3表面与自身的乘积上提供了显著的二维代数循环，以及K3表面与自身的对应关系。当具有给定Mukai矢量的K3表面上相干轴的模与K3表面重合时，就会发生这种情况。我们想详细研究这一现象。