Counting Higgs bundles and type $A$ quiver bundles
Counting Higgs bundles and type $A$ quiver bundles
复制标题
计算希格斯束和 $A$ 型箭袋束
作者：
S. Mozgovoy;O. Schiffmann
我们证明了一个封闭的公式计数半稳定扭曲（或亚纯）Higgs丛的固定秩和度的光滑射影曲线的亏格$g$定义在一个有限域上，当扭曲线丛度至少是2g-2$（这包括通常的Higgs丛的情况下）。这就产生了扭曲希格斯包模空间的唐纳森-托马斯不变量的封闭表达式。我们同样处理扭曲的A$型（有限或仿射），获得特别是一个Harder-Narasimhan型公式计数半稳定的U（p，q）$-Higgs束在一个光滑的投影曲线定义在一个有限域。
We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type $A$ (finite or affine), obtaining in particular a Harder–Narasimhan-type formula counting semistable $U(p,q)$-Higgs bundles over a smooth projective curve defined over a finite field.
关于链和希格斯丛模的动机
DOI：
10.4171/jems/494
发表时间：
2014
期刊：
arXiv: Algebraic Geometry
影响因子：
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作者：
Oscar García–Prada;Jochen Heinloth;Alexander Schmitt
通讯作者：
Alexander Schmitt