Hilbert's 14th Problem and Cox Rings

Details Hilbert's 14th Problem and Cox Rings Hilbert's 14th Problem and Cox Rings

2005-05-16

arxiv.org/abs/math/0505337v2

Mathematics

Algebraic Geometry

20 pages; final version, Compositio Math. Vol.142 (2006)

Scientific paper

Our main result is the description of 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 we show that the algebra of invariants of the action of a two-dimensional vector group introduced by Nagata is finitely generated by certain explicit determinants. We also prove the finite generation of the algebras of invariants of actions of vector groups related to T-shaped Dynkin diagrams introduced by Mukai.

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