Severi varieties of projective surfaces
Speaker: Adrian Zahariuc (U. Windsor)
Abstract: Severi varieties are spaces which parametrize projective plane curves of fixed degree and geometric genus, and this definition may be easily extended to other projective surfaces by taking the spaces which parametrize curves of fixed homology class and geometric genus on the given surface. In this talk, I will first give a gentle and concrete introduction to these objects, and then I will focus on a question which (although known for the projective plane) is still open for most other projective surfaces, namely the question of whether the Severi varieties are irreducible. This question can be rephrased as follows: is it possible to continuously deform any curve on the surface into any other curve on the surface of the same homology class and geometric genus while keeping the genus fixed throughout the deformation?
Math & Stats Zoom Room
This is part of the Department of Mathematics & Statistics Colloquium series.