Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces
Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces
复制标题
（堆叠）Hirzebruch 曲面上框架滑轮模空间的庞加莱多项式
DOI：
10.1007/s00220-011-1231-z
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发表时间：
2009
影响因子：
2.4
通讯作者：
A. Tanzini
中科院分区：
文献类型：
--
作者：
U. Bruzzo;R. Poghossian;A. Tanzini
利用局部化技术研究了Hirzebruch曲面上框架无挠层的模空间。在Huybrechts-Lehn框架模理论的框架下，讨论了这类模空间的一些一般性质.我们对模空间上的复曲面作用下的不动点进行分类，并使用它来计算后者的庞加莱多项式。这意味着我们所考虑的模空间是不可约的。我们还考虑分数的第一陈类，这意味着我们将我们的计算扩展到Hirzebruch表面的堆叠变形。从物理的角度来看，我们的结果提供了一个计算D4-D2-D 0膜束缚态的数学框架。
We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincaré polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the mathematical framework for the counting of D4-D2-D0 branes bound states on total spaces of the bundles $${\mathcal {O}_{\mathbb {P}^1}(-p)}$$ .