OSU Mathematics Seminars and Colloquia
Wed, Oct 07, 2020
Topology Seminar
3:45 PM
Virtual meeting
Some results on the local topology of algebraic sets
Achinta Nandi, Oklahoma State University
Host: Neil Hoffman
Contact Neil Hoffman or Henry Segerman for the meeting link.
[Abstract] [PDF]
Abstract: The topology of an algebraic set near a singular point is of fundamental interest in the study of analytic varieties. In this talk, we shall investigate the local topology of an algebraic set. After a brief description of the basics, we will prove some general facts about algebraic sets and establish results about the local topology of an algebraic set near regular points. A fundamental lemma concerning the existence of real analytic curves on the real algebraic sets will be proved to conclude the talk. Time permitting, we shall discuss some applications of the said lemma, in particular, a fibration theorem which is useful in describing the local topology near singular points. The talk is based on John Milnor's "Singular points of complex hypersurfaces".
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