复解析空间上的L2上同调

射影复流形上的L2理论在近年来得到广泛应用，如T. Y. Siu的invariance of plurigenera、S.Boucksom, J.P.Demailly，M.Păun，T. Peternell在Mumford猜想上的突破、J .Y. Cao与M. Păun在Abel簇上Itaka猜想上的突破以及周向宇团队在L2分析上的新进展。近几十年复几何与代数几何的发展迫使人们注意到研究带奇点空间的重要性。然而相比于光滑情形，复解析空间上的L2理论尚未得到充分的发展。本课题希望在近些年发展的基础上，研究紧Kahler空间上的L2-Hodge理论，并将L2技术用于带奇点射影代数簇的几何研究。

The L2 theory on complex projective manifolds has been widely used in recent years, such as T. Y. Siu's invariance of plurigenera, S.Boucksom, J.P.Demailly，M.Păun，T. Peternell's breakthrough in Mumford's conjecture, J .Y. Cao and M. Păun's work on itaka's conjecture over abelian varieties and the pioneering works of Xiangyu Zhou's group. The developments of complex geometry and algebraic geometry in recent decades has forced people to pay attention to the importance of studying spaces with singularities. However, compared with the smooth case, the L2 theory in complex analytic spaces has not been fully developed. Based on the development in recent years, this project hopes to study the L2-Hodge theory on compact Kahler spaces, and to apply the L2 technique to the geometric research of singular projective algebraic varieties.