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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

13 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	353-372
Número de páginas	20
Publicación	Journal of Algebra
Volumen	322
N.º	2
DOI	https://doi.org/10.1016/j.jalgebra.2009.04.020
Estado	Publicada - 15 jul. 2009
Publicado de forma externa	Sí

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10.1016/j.jalgebra.2009.04.020

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title = "Picard-graded Betti numbers and the defining ideals of Cox rings",

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.",

keywords = "Cox rings, Del Pezzo surfaces, Multigraded Betti numbers",

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T1 - Picard-graded Betti numbers and the defining ideals of Cox rings

AU - Laface, Antonio

AU - Velasco, Mauricio

PY - 2009/7/15

Y1 - 2009/7/15

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

UR - http://www.scopus.com/inward/record.url?scp=68649101774&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2009.04.020

DO - 10.1016/j.jalgebra.2009.04.020

M3 - Artículo

AN - SCOPUS:68649101774

SN - 0021-8693

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

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