Geometry & Topology Seminar

Ethan Cotterill, University of Campinas

"Cuspidal curves in P^n, and partition arithmetic"

The irreducibility the Severi variety of plane curves V_{d,g} of fixed degree d and arithmetic genus g is a well-known and celebrated result of J. Harris from the 1980s. In higher (ambient) dimension, the situation changes drastically, and (the natural generalizations of) Severi varieties of curves with fixed numerical invariants in P^n are very often reducible and have components of larger-than-expected dimensions. In this talk, I will explain why this is the case, on the basis of a combinatorial analysis of unicuspidal rational curves with fixed ramification profiles.

MC 5417