### Algebra SeminarMeasures of irrationality for algebraic varietiesBrooke Ullery (Harvard University)

Wednesday, April 3, 2019
11:15am – 12:05pm

Storrs Campus
Monteith, 313

A smooth algebraic curve is said to be rational if it is isomorphic to P^1, the projective line. More generally, the gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. The intuition is that the higher the gonality, the further the curve is from being rational. A classical theorem of Noether says that if C is a smooth plane curve of degree d, then the gonality of C is d-1, and it is obtained by projecting away from a point on the curve. A natural question is: does Noether's theorem generalize in some way to curves in larger projective spaces? What about to higher dimensional varieties? We will explore these questions, focusing on the examples of hypersurfaces and, more generally, complete intersections in projective space.

Contact:

Mihai Fulger, mihai.fulger@uconn.edu

Algebra Seminar (primary), UConn Master Calendar