Vector bundles on genus 2 curves and trivectors
Vector bundles on genus 2 curves and trivectors
复制标题
属 2 曲线和三向量上的向量丛
作者：
E. Rains;Steven V. Sam
给定一个2属的复曲线C，在C上的3阶半稳定束的模空间和一个被称为Coble立方的三次超曲面之间存在着众所周知的关系。其中的一些方面已知与9维复向量空间的三次外幂的几何不变性理论有关。我们将这种关系推广到任意域，并研究了与不变量理论的一些联系，这将在后续论文中进行更深入的研究。
Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space. We extend this relationship to arbitrary fields and study some of the connections to invariant theory, which will be studied more in-depth in a followup paper.