Toric ideals of simple surface singularities

Gülay Kaya; Pınar Mete; Mesut Sahin

doi:10.15672/HJMS.2015449094

Toric ideals of simple surface singularities

Gülay Kaya
, Pınar Mete
, Mesut Sahin

Galatasaray University
Balikesir University
Çankiri Karatekin University

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

Abstract

In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gröbner bases for these toric ideals that are also minimal generating sets consisting of large number of binomials of degree ≤ 4. In particular, they give rise to squarefree initial ideals as well.

Original language	English
Pages (from-to)	1057-1069
Number of pages	13
Journal	Hacettepe Journal of Mathematics and Statistics
Volume	44
Issue number	5
DOIs	https://doi.org/10.15672/HJMS.2015449094
Publication status	Published - 2015
Externally published	Yes

Keywords

Semigroup of Lipman
Simple surface singularities
Toric ideals

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10.15672/HJMS.2015449094

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abstract = "In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gr{\"o}bner bases for these toric ideals that are also minimal generating sets consisting of large number of binomials of degree ≤ 4. In particular, they give rise to squarefree initial ideals as well.",

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AU - Mete, Pınar

AU - Sahin, Mesut

PY - 2015

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AB - In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gröbner bases for these toric ideals that are also minimal generating sets consisting of large number of binomials of degree ≤ 4. In particular, they give rise to squarefree initial ideals as well.

KW - Semigroup of Lipman

KW - Simple surface singularities

KW - Toric ideals

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JF - Hacettepe Journal of Mathematics and Statistics

IS - 5

ER -

Toric ideals of simple surface singularities

Abstract

Keywords

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