Hilbert's 14th problem and Cox rings
By Ana-Maria Castravet, Jenia Tevelev. Compositio Mathematica, 2005
118 citations recorded by the source corpus.
Our main result is the description of generators of the total coordinate ring of the blow-up of $\mathbb{P}^n$ 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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d060d233e274933b932a349c01bafd4991504b4d
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In Algebra and Number Theory
- B. Totaro
- Bernd Sturmfels
- Zhiqiang Xu
- Eric Katz
- Sam Payne
- Federico Ardila
- Jenia Tevelev
- Claire Voisin
In Geometry and Topology
- B. Totaro
- Bernd Sturmfels
- Zhiqiang Xu
- Sam Payne
- Max Lieblich
- Eric Katz
- Federico Ardila
- Philipp Gross
Citations in the corpus
- Sagbi Bases of Cox-Nagata Rings (2008, methodology): “[8, 24] Suppose that G is a generic subspace of codimension d in K.”
- Singular del Pezzo surfaces whose universal torsors are hypersurfaces (2006, unknown): “[HK00], [Muk01], [BH03a], [BH03b], [EKW04], [CT05].”
- The cone conjecture for Calabi-Yau pairs in dimension two (2009, methodology): “Therefore X has finitely generated Cox ring, as Galindo-Monserrat [13, Corollary 3.3], Castravet-Tevelev [7] and Mukai [28] proved by other methods.”