Mathmatics Colloquium - ""Severi varieties of projective surfaces"
Speaker : Adrian Zahariuc , University of Windsor,
Adrian's interest are in algebraic geometry, with a particular focus on classical questions as well as enumerative geometry. He is a former student of Joe Harris, a world-renowned algebraic geometer at Harvard University who is also known for his several well-written books on the subject.
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?
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Ellen LynchMathmatics Colloquium - ""Severi varieties of projective surfaces"