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

Access to Document

10.1016/j.jalgebra.2009.04.020

Cite this

@article{7e62576484d444348a95cf41ee717924,

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",

author = "Antonio Laface and Mauricio Velasco",

year = "2009",

month = jul,

day = "15",

doi = "10.1016/j.jalgebra.2009.04.020",

language = "Ingl{\'e}s",

volume = "322",

pages = "353--372",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

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 - https://www.scopus.com/pages/publications/68649101774

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this