Upper bounds for dimensions of singularity categories

Hailong Dao; Ryo Takahashi

doi:10.1016/j.crma.2015.01.012

Homological algebra/Algebraic geometry

Upper bounds for dimensions of singularity categories

Presented by: Claire Voisin

Hailong Dao ¹; Ryo Takahashi ^2,³

¹ Department of Mathematics, University of Kansas, Lawrence, KS 66045-7523, USA
² Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
³ Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA

Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 297-301.

Abstract
Résumé

This paper gives upper bounds for the dimension of the singularity category of a Cohen–Macaulay local ring with an isolated singularity. One of them recovers an upper bound given by Ballard, Favero and Katzarkov in the case of a hypersurface.

Cet article donne des bornes supérieures pour la dimension de la catégorie de singularité d'un anneau local Cohen–Macaulay à singularité isolée. L'une de nos estimations redonne une borne fournie par Ballard, Favero et Katzarkov dans le cas des hypersurfaces.

Received: 2014-07-13
Accepted: 2015-01-23
Published online: 2015-02-25

DOI: 10.1016/j.crma.2015.01.012

Author's affiliations:

Hailong Dao ¹; Ryo Takahashi ^{2, 3}

¹ Department of Mathematics, University of Kansas, Lawrence, KS 66045-7523, USA
² Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
³ Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA

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     title = {Upper bounds for dimensions of singularity categories},
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     pages = {297--301},
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     volume = {353},
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     year = {2015},
     doi = {10.1016/j.crma.2015.01.012},
     language = {en},
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Hailong Dao; Ryo Takahashi. Upper bounds for dimensions of singularity categories. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 297-301. doi : 10.1016/j.crma.2015.01.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.012/

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