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

Mike Stillman; Damiano Testa; Mauricio Velasco

doi:10.1016/j.jalgebra.2007.05.016

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

Mike Stillman
, Damiano Testa
, Mauricio Velasco

Cornell University

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We introduce the notion of monomial group action and study some of its consequences for Gröbner 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 ≥3) as quotients of a polynomial ring by an ideal generated by quadrics.

Original language	English
Pages (from-to)	777-801
Number of pages	25
Journal	Journal of Algebra
Volume	316
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2007.05.016
State	Published - 15 Oct 2007
Externally published	Yes

Keywords

Cox rings
Del Pezzo surfaces
Grobner bases

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10.1016/j.jalgebra.2007.05.016

Cite this

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abstract = "We introduce the notion of monomial group action and study some of its consequences for Gr{\"o}bner 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 ≥3) as quotients of a polynomial ring by an ideal generated by quadrics.",

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AU - Stillman, Mike

AU - Testa, Damiano

AU - Velasco, Mauricio

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Y1 - 2007/10/15

N2 - We introduce the notion of monomial group action and study some of its consequences for Gröbner 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 ≥3) as quotients of a polynomial ring by an ideal generated by quadrics.

AB - We introduce the notion of monomial group action and study some of its consequences for Gröbner 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 ≥3) as quotients of a polynomial ring by an ideal generated by quadrics.

KW - Cox rings

KW - Del Pezzo surfaces

KW - Grobner bases

UR - https://www.scopus.com/pages/publications/34548664370

U2 - 10.1016/j.jalgebra.2007.05.016

DO - 10.1016/j.jalgebra.2007.05.016

M3 - Artículo

AN - SCOPUS:34548664370

SN - 0021-8693

VL - 316

SP - 777

EP - 801

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

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

Abstract

Keywords

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