Algebraic Geometry Seminar

I report on ongoing joint work with Mihail Grinberg. We introduce the notion of a self-indexing flag of closed subspaces relative to a Whitney stratification of a complex algebraic variety. This is a notion that is related to and is in fact inspired by the classical notion of a self-indexing Morse function. We use this notion to give a rather concrete description of cohomology with coefficients in complexes of sheaves with constructible cohomology sheaves. "Concrete" here refers to the construction of an explicit complex of abelian groups that computes this cohomology as well as other structures, such as the perverse filtration. We name these complexes Morse-Beilinson complexes as they are akin to the Morse complex and use constructions based on Beilinson's Basic Lemma. Speaker(s): Mark de Cataldo (Stony Brook University)