摘要翻译:
ADHM构造用复向量空间范畴中的关系在射影平面上的框架无扭束和颤振的稳定框架表示之间建立了一一对应关系。本文研究了光滑复射影曲线$x$上相干束的阿贝尔范畴中的同颤振表示的模空间的几何性质。特别地,通过Pandharipande和Thomas的稳定对,证明了该模空间实际上是光滑的,并通过相对Beilinson谱序列与曲线计数结构相关。这给出了局部Donaldson-Thomas曲线理论的一个新的猜想构造和一个自然的高阶推广。
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英文标题:
《Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory》
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作者:
Duiliu-Emanuel Diaconescu
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最新提交年份:
2012
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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:Physics 物理学
二级分类:High Energy Physics - Theory 高能物理-理论
分类描述:Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论,超对称性和超引力。
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英文摘要:
The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper studies the geometry of moduli spaces of representations of the same quiver with relations in the abelian category of coherent sheaves on a smooth complex projective curve $X$. In particular it is proven that this moduli space is virtually smooth and related byrelative Beilinson spectral sequence to the curve counting construction via stable pairs of Pandharipande and Thomas. This yields a new conjectural construction for the local Donaldson-Thomas theory of curves as well as a natural higher rank generalization.
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PDF链接:
https://arxiv.org/pdf/0801.0820