Hilbert's 14th problem and Cox rings
AM Castravet, J Tevelev - Compositio Mathematica, 2006 - cambridge.org
Compositio Mathematica, 2006•cambridge.org
Our main result is the description of generators of the total coordinate ring of the blow-up of
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.
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.
Our main result is the description of generators of the total coordinate ring of the blow-up of 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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