论文标题
在投影Deligne-Mumford堆栈上的可分离对的模量空间
Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
论文作者
论文摘要
我们概括了构建可半固定对的模量空间的形态的参数化同构类别，从固定的连贯的捆到任何具有固定希尔伯特多项式的捆的捆，在对投射Deligne-Mummord堆栈的情况下，固定的Hilbert多项式概念。我们研究稳定对的变形和阻塞理论，然后证明在二维和三个方面的某些情况下存在虚拟基本类别。这导致了三维光滑的投影式磨难蒙福堆堆栈中pandharipande-thomas不变的定义。
We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective Deligne-Mumford stacks. We study the deformation and obstruction theories of stable pairs, and then prove the existence of virtual fundamental classes for some cases of dimension two and three. This leads to a definition of Pandharipande-Thomas invariants on three-dimensional smooth projective Deligne-Mumford stacks.
