## Hilbert's 14-th Problem and Cox rings

Ana-Maria Castravet, University of Texas

Abstract:

I will describe generators of the total coordinate ring of the blow-up of
$P^n$ in any number of points that lie on a rational normal
curve. As a corollary, I will show that the algebra of invariants of an
action of the two-dimensional additive group introduced by Nagata is
finitely generated by certain explicit determinants. The finite generation
of certain algebras of invariants of actions of additive groups related to
T-shaped Dynkin diagrams introduced by Mukai also follows. This is joint
work with E. Tevelev.