From: Brenda Cook (brenda@math.missouri.edu)
Date: Tue Dec 05 2006 - 13:20:02 CST
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Prof. Nikita Netsvetaev
St. Petersburg State University
On the Topological Structure of Complex Projective Varieties with Simple
Singularities
Abstract Unlike the real field case, the topology of many nonsingular
complex projective varieties is controlled to a large extent by the
basic homotopy information, the latter being often determined by simple
numerical data, like the dimension (sine qua non, to be sure) and the
degrees of equations.The corresponding results are eventually related to
Lefschetz type phenomena and their topological consequences.
In the presence of singularities, even isolated, the situation becomes
much more diverse, though not unfeasible. As the simplest example, which
is however very far from being trivial, we can consider complex
hypersurfaces with, say, quadratic singularities and prescribed set of
singular points. This data are easily seen to determine the topology of
the hypersurface, but only implicitly. Under certain restrictions on the
degree, we can give a precise topological description of such a
hypersurface by means of decomposing it into a connected sum. In this
case, the topological type of the hypersurface is determined by its
dimension, degree, and the number of singular points.
3:30-4:20 p.m.
Thursday, December 7
105 General Classroom Building
Refreshments will be served at 3:00 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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