Geodesic
Classification of singularities of cluster algebras of finite type: the case of trivial coefficients
Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 170-204

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DOI

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.
DOI : 10.1017/S0017089522000209
Mots-clés : cluster algebras, continuant polynomials, singularities, resolution of singularities 
Benito, Angelica; Faber, Eleonore; Mourtada, Hussein; Schober, Bernd. Classification of singularities of cluster algebras of finite type: the case of trivial coefficients. Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 170-204. doi: 10.1017/S0017089522000209
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     title = {Classification of singularities of cluster algebras of finite type: the case of trivial coefficients},
     journal = {Glasgow mathematical journal},
     pages = {170--204},
     year = {2023},
     volume = {65},
     number = {1},
     doi = {10.1017/S0017089522000209},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000209/}
}
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