Colloquium: On the complexity of curves in complete intersections

Abstract: A surface X in CP³ cut out by the homogeneous polynomial F = x² + y² + z² + w² = 0 contains a 1-dimensional family of lines. If one replaces F with a general cubic equation, then there are famously a finite number of lines (27). What happens if we increase the degree of F further? What are the curves on X with minimal invariants? We will answer this question and its generalizations. Time permitting, we will explain the connection to certain birational invariants called measures of irrationality.

Host: John Shareshian

A Tea will follow in Cupples 1 in the Lounge from 2:00 – 3:00p.