Picard-graded Betti numbers and the defining ideals of Cox rings

Antonio Laface; Mauricio Velasco

doi:10.1016/j.jalgebra.2009.04.020

Picard-graded Betti numbers and the defining ideals of Cox rings

Antonio Laface, Mauricio Velasco

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

13 Scopus citations

Abstract

We introduce a complex of vector spaces whose homology determines the Picard-graded Betti numbers of the Cox ring of a Mori Dream Space. As an application of this construction we prove a conjecture of Batyrev and Popov which describes presentations for the Cox rings of Del Pezzo surfaces of degree at least two.

Original language	English
Pages (from-to)	353-372
Number of pages	20
Journal	Journal of Algebra
Volume	322
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2009.04.020
State	Published - 15 Jul 2009
Externally published	Yes

Keywords

Cox rings
Del Pezzo surfaces
Multigraded Betti numbers

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10.1016/j.jalgebra.2009.04.020

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abstract = "We introduce a complex of vector spaces whose homology determines the Picard-graded Betti numbers of the Cox ring of a Mori Dream Space. As an application of this construction we prove a conjecture of Batyrev and Popov which describes presentations for the Cox rings of Del Pezzo surfaces of degree at least two.",

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AU - Laface, Antonio

AU - Velasco, Mauricio

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N2 - We introduce a complex of vector spaces whose homology determines the Picard-graded Betti numbers of the Cox ring of a Mori Dream Space. As an application of this construction we prove a conjecture of Batyrev and Popov which describes presentations for the Cox rings of Del Pezzo surfaces of degree at least two.

AB - We introduce a complex of vector spaces whose homology determines the Picard-graded Betti numbers of the Cox ring of a Mori Dream Space. As an application of this construction we prove a conjecture of Batyrev and Popov which describes presentations for the Cox rings of Del Pezzo surfaces of degree at least two.

KW - Cox rings

KW - Del Pezzo surfaces

KW - Multigraded Betti numbers

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DO - 10.1016/j.jalgebra.2009.04.020

M3 - Artículo

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VL - 322

SP - 353

EP - 372

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Picard-graded Betti numbers and the defining ideals of Cox rings

Abstract

Keywords

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