Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

Details Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

2006-10-08

arxiv.org/abs/math/0610261v1

Mathematics

Commutative Algebra

29 pages, 3 figures

Scientific paper

We introduce the notion of monomial group action and study some of its
consequences for Groebner basis theory. As an application we prove a conjecture
of V. Batyrev and O. Popov describing the Cox rings of Del Pezzo surfaces (of
degree at least 3) as quotients of a polynomial ring by an ideal generated by
quadrics.

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