Hilbert's thirteenth problem and the moduli space of abelian varieties
By Mark Kisin
Appears in collection : Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
The (multi-valued) solution of a general polynomial of degree n is a priori a function of n-1 variables. Hilbert's thirteenth problem and its variants ask when such functions can be written as a composite of functions in a smaller number of variables. I will explain some progress on this question which uses the geometry of A_g.This is joint work with Benson Farb and Jesse Wolfson.
