Hilbert's 14-th Problem and Cox rings
Ana-Maria Castravet, University of Texas

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.