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The irreducibility of the generalized Severi varieties

Algebraic Geometry

Speaker: Adrian Zahariuc, UC Davis
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Location: 2112 MSB
Start time: Wed, Nov 8 2017, 11:00AM

The Severi varieties are roughly the (quasi-)projective varieties parametrizing plane curves of fixed degree and geometric genus. A theorem of Harris from the mid 80s states that they are irreducible. The main goal of the talk is to discuss an alternative proof and generalization of this statement by proving inductively that the so-called generalized Severi varieties introduced by Caporaso and Harris (or rather a slight variant of them) are irreducible.