轨形的形变与McKay对应

受到Vafa与Witten的一个例子的启发，在这个项目中，我们将跟随Căldăraru的建议，使用Hochschild上同调来研究轨形的形变。对于轨形的二阶Hochschild上同调在HKR分解下的直和项，我们将几何地刻画它们所描述的轨形的一阶形变。一个处理discrete torsion的扭的（twisted）版本也在考虑范围内。另外，我们还将研究在Mckay对应下轨形的形变的与它的crepant解消的形变之间的对应。我们的研究将对理解轨形的从弦理论角度所容许的形变有帮助。这个研究同样将为计算一簇复轨形的周期提供理论基础（这在镜对称中经常出现）。

In this project, inspired by Vafa and Witten's example, we are going to study deformations of orbifolds by using Hochschild cohomology following the suggestion of Căldăraru. We are going to describe geometrically the first order deformations of orbifolds parametrized by the direct summands in the HKR decomposition of the second Hochschild cohomology group. A twisted version concerning the existence of discrete torsion will also be considered. Moreover, we are also going to study the correspondence between orbifold deformations and the deformations of its crepant resolution under Mckay correspondence. Our study will help to understand the allowable deformations of orbifold from the point of view of string theory. This research will also provide a foundation for computing the periods of a family of complex orbifolds which occurs frequently in mirror symmetry.