Classification of singularities of cluster algebras of finite type: the case of trivial coefficients

被引：0

作者：

Benito, Angelica ^{[1
]}

Faber, Eleonore ^{[2
]}

Mourtada, Hussein ^{[3
,4
]}

Schober, Bernd ^{[5
]}

机构：

[1] Univ Autonoma Madrid, Fac Formac Prof, Dept Didact Especif, Madrid 28049, Spain

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

[3] Univ Paris Cite, Batiment Sophie Germain,Case 7012, F-75205 Paris 13, France

[4] Sorbonne Univ, CNRS, IMJ PRG, Batiment Sophie Germain,Case 7012, F-75205 Paris 13, France

[5] Carl Von Ossietzky Univ Oldenburg, Inst Math, Ammerlander Heerstr 114-118, D-26129 Oldenburg, Oldb, Germany

来源：

GLASGOW MATHEMATICAL JOURNAL | 2023年 / 65卷 / 01期

关键词：

cluster algebras; continuant polynomials; singularities; resolution of singularities; GEOMETRY;

D O I：

10.1017/S0017089522000209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of these singularities via blowups in regular centers over fields of arbitrary characteristic. Furthermore, from the same perspective, we study a family of cluster algebras which are not of finite type and which arise from a star shaped quiver.

引用

页码：170 / 204

页数：35

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