Hilbert functions of Cox rings of del Pezzo surfaces

Jinhyung Park; Joonyeong Won

doi:10.1016/j.jalgebra.2017.02.028

Hilbert functions of Cox rings of del Pezzo surfaces

Jinhyung Park, Joonyeong Won

Department of Mathematics

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

Abstract

To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green–Lazarsfeld indices, the projective dimensions, and the Castelnuovo–Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.

Original language	English
Pages (from-to)	309-331
Number of pages	23
Journal	Journal of Algebra
Volume	480
DOIs	https://doi.org/10.1016/j.jalgebra.2017.02.028
State	Published - 15 Jun 2017

Bibliographical note

Funding Information:
The second author has been supported by the National Research Foundation of Korea (NRF-2014R1A1A2056432) and IBS-R003-D1.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Cox ring
Del Pezzo surface
Hilbert function
Syzygy

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10.1016/j.jalgebra.2017.02.028

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title = "Hilbert functions of Cox rings of del Pezzo surfaces",

abstract = "To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green–Lazarsfeld indices, the projective dimensions, and the Castelnuovo–Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.",

keywords = "Cox ring, Del Pezzo surface, Hilbert function, Syzygy",

author = "Jinhyung Park and Joonyeong Won",

note = "Funding Information: The second author has been supported by the National Research Foundation of Korea (NRF-2014R1A1A2056432) and IBS-R003-D1. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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doi = "10.1016/j.jalgebra.2017.02.028",

language = "English",

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T1 - Hilbert functions of Cox rings of del Pezzo surfaces

AU - Park, Jinhyung

AU - Won, Joonyeong

PY - 2017/6/15

Y1 - 2017/6/15

N2 - To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green–Lazarsfeld indices, the projective dimensions, and the Castelnuovo–Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.

AB - To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green–Lazarsfeld indices, the projective dimensions, and the Castelnuovo–Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.

KW - Cox ring

KW - Del Pezzo surface

KW - Hilbert function

KW - Syzygy

UR - http://www.scopus.com/inward/record.url?scp=85015957845&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.02.028

DO - 10.1016/j.jalgebra.2017.02.028

M3 - Article

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SN - 0021-8693

VL - 480

SP - 309

EP - 331

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hilbert functions of Cox rings of del Pezzo surfaces

Abstract

Bibliographical note

Keywords

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