Remarks on the stack of coherent algebras
Remarks on the stack of coherent algebras
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关于相干代数栈的评论
DOI：
10.1155/imrn/2006/75273
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发表时间：
2006
影响因子：
1
通讯作者：
Max Lieblich
中科院分区：
文献类型：
--
作者：
Max Lieblich
考虑具有适当支持的相干代数堆，一个将Alexeev和Knutson的分支变体堆推广到Artin堆的模问题。主要的结果是证明了比目前已知的更普遍的Quot和Hom空间的存在性，以及对Alexeev和Knutson的原始构造的几个应用：证明了分支变体的堆栈总是代数的，一维族的极限总是存在的，以及在环境堆栈上的某些假设下，分支变体堆栈的连接分量在基上是固有的。
We consider the stack of coherent algebras with proper support, a moduli problem generalizing Alexeev and Knutson's stack of branchvarieties to the case of an Artin stack. The main results are proofs of the existence of Quot and Hom spaces in greater generality than is currently known and several applications to Alexeev and Knutson's original construction: a proof that the stack of branchvarieties is always algebraic, that limits of one-dimensional families always exist, and that the connected components of the stack of branchvarieties are proper over the base under certain hypotheses on the ambient stack.