Arithmetic Geometry and Number Theory RTG Seminar: Low degree points on families of curves

Seminar | September 24 | 3:10-5 p.m. | 784 Evans Hall

 Isabel Vogt, MIT

 Department of Mathematics

It is a classical theorem of Max Noether that the (geometric) gonality of a smooth plane curve of degree $d$ is $d-1$, and all minimal degree maps come from projection from a point on the curve. Debarre and Klassen proved an arithmetic strengthening of this result when the curve is defined over a number field: if $d \geq 8$, there are only finitely many algebraic points with residue degree strictly less than $d-1$. I will discuss extensions of this result to sufficiently ample curve classes on any surface with trivial irregularity. This is joint work with Geoffrey Smith.