摘要翻译:
给出了代数空间上$\pgl_n$-torsors(Azumaya代数)的一个紧致栈的方法。特别地,当周围空间是光滑射影曲面时,我们用我们的方法证明了各种模空间是不可约的,并且带有自然的虚基类。我们还证明了Skolem-Noether定理的一个版本,它允许我们给出紧化模问题中边界点的显式描述。
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英文标题:
《Compactified moduli of projective bundles》
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作者:
Max Lieblich
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Representation Theory 表象理论
分类描述:Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示,李理论,结合代数,多重线性代数
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英文摘要:
We present a method for compactifying stacks of $\PGL_n$-torsors (Azumaya algebras) on algebraic spaces. In particular, when the ambient space is a smooth projective surface we use our methods to show that various moduli spaces are irreducible and carry natural virtual fundamental classes. We also prove a version of the Skolem-Noether theorem for certain algebra objects in the derived category, which allows us to give an explicit description of the boundary points in our compactified moduli problem.
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PDF链接:
https://arxiv.org/pdf/0706.1311