手性德拉姆复形中的若干问题

本项目主要研究手性德拉姆复形及其上同调。具体包括：.（A）闭复流形特别是卡拉比-丘流形和厄米特局部对称空间的手性德拉姆复形的整体截面；.（B）闭复流形特别是HyperKähler流形的手性霍奇上同调的性质及其在椭圆亏格和月光理论中的应用。

In this project, we will study the chiral de Rham complex and its cohomology, including:.(A) the global sections of the chiral de Rham complexes on closed complex manifolds, especially, on Calabi-Yau manifolds and Hermitian locally symmetric spaces..(B) the properties of the chiral Hodge cohomology on closed complex manifolds, especially on HyperKähler manifolds, and their applications in elliptic genus and moonshine theory.