Mathematical Sciences: L2-Cohomolgy of Singular Spaces

点击翻译按钮获取中文摘要

The principal investigator will extend (in both complex analytic and Lie theoretic directions) his previous work on analytically representing intersection cohomology of singular spaces by L2-cohomology. In particular, he proposes to find complete Kaehler metrics on the smooth locus of projective varieties whose L2-cohomology represents the intersection cohomology of the singular variety. The principal investigator will extend ideas used in his solution to the Zucker conjecture to the case of complete Kaehler metrics. This conjecture stated that except in certain specified cases, the L2- and intersection cohomology were essentially the same. Cohomology is the dual of homology. Thus, cohomology consists of a sequence of groups of functions which are tied together by a sequence of "co-boundary" functions. These structures have been used to catalog hypersurfaces of many dimensions.