Mathematical Sciences: Cycles, Residues & Global Problems in Geometry

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9505174 Lawson The proposed research lies at the interface of algebraic geometry and algebraic topology. A principal goal is to further develop the theory of algebraic cycles on projective varieties: this theory, largely founded by Lawson, seeks to understand projective varieties from a topological standpoint, and can be considered as a generalization of the theory of schemes. An algebraic variety is defined as the common zero set of a collection of homogeneous polynomials in several variables; algebraic geometry is the study of algebraic varieties (or what is the same, homogeneous polynomial equations in several complex variables). The proposed research has to do with applying topological tools to study various subsets of algebraic varieties.