Moduli of toric vector bundles
Moduli of toric vector bundles
复制标题
复曲面向量丛的模
作者：
S. Payne
摘要给出了具有固定等变全Chern类的环状向量丛的模叠，它是由线性群作用构成的框丛的精细模格式的商。该精细模方案被显式地描述为由组合指定的等级条件切割出的部分标志变体的乘积的局部闭合子方案。利用这个刻划，我们证明了在Vakil意义下，秩为3的环向量丛的模满足Murphy定律。本文的前言部分对Klyachko对环向量丛的分类作了详尽的介绍。
Abstract We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that the moduli of rank three toric vector bundles satisfy Murphy’s law, in the sense of Vakil. The preliminary sections of the paper give a self-contained introduction to Klyachko’s classification of toric vector bundles.