Comptes Rendus
Article de recherche - Géométrie algébrique
Deformations over non-commutative base
[Déformations sur une base non-commutative]
Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 159-169.

Nous faisons quelques remarques sur la théorie des déformations sur des bases non commutatives. Nous décrivons l’algèbre de base des déformations non commutatives semi-universelles à l’aide des espaces vectoriels T 1 et T 2 .

We make some remarks on deformation theory over non-commutative base. We describe the base algebra of semi-universal non-commutative deformations using vector spaces T 1 and T 2 .

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DOI : 10.5802/crmath.622
Classification : 14D15, 32G05

Yujiro Kawamata 1

1 Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Deformations over non-commutative base},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {159--169},
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     year = {2024},
     doi = {10.5802/crmath.622},
     language = {en},
}
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Yujiro Kawamata. Deformations over non-commutative base. Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 159-169. doi : 10.5802/crmath.622. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.622/

[1] Agnieszka Bodzenta; Alexey Bondal Flops and spherical functors, Compos. Math., Volume 158 (2022) no. 5, pp. 1125-1187 | DOI | MR | Zbl

[2] Will Donovan; Michael Wemyss Noncommutative deformations and flops, Duke Math. J., Volume 165 (2016) no. 8, pp. 1397-1474 | MR | Zbl

[3] Eivind Eriksen; Olav Arnfinn Laudal; Arvid Siqveland Noncommutative Deformation Theory, Monographs and Research Notes in Mathematics, CRC Press, 2017 | DOI

[4] Zheng Hua; Yukinobu Toda Contraction algebra and invariants of singularities, Int. Math. Res. Not., Volume 2018 (2018) no. 10, pp. 3173-3198 | MR | Zbl

[5] Sheldon Katz Genus zero Gopakumar-Vafa invariants of contractible curves, J. Differ. Geom., Volume 79 (2008) no. 2, pp. 185-195 | MR | Zbl

[6] Yujiro Kawamata On multi-pointed non-commutative deformations and Calabi-Yau threefolds, Compos. Math., Volume 154 (2018) no. 9, pp. 1815-1842 | DOI | MR | Zbl

[7] Yujiro Kawamata Non-commutative deformations of simple objects in a category of perverse coherent sheaves, Sel. Math., New Ser., Volume 26 (2020) no. 3, 43, 22 pages | MR | Zbl

[8] Yujiro Kawamata On non-commutative formal deformations of coherent sheaves on an algebraic variety, EMS Surv. Math. Sci., Volume 8 (2021) no. 1-2, pp. 237-263 | DOI | MR | Zbl

[9] Olav A. Laudal Noncommutative deformations of modules, Homology Homotopy Appl., Volume 4 (2002) no. 2, pp. 357-396 | DOI | MR | Zbl

[10] Michael Schlessinger Functors of Artin rings, Trans. Am. Math. Soc., Volume 130 (1968) no. 2, pp. 208-222 | DOI | MR | Zbl

[11] Edoardo Sernesi Deformations of Algebraic Schemes, Grundlehren der Mathematischen Wissenschaften, 334, Springer, 2006, xi+339 pages

[12] Yukinobu Toda Non-commutative width and Gopakuma–Vafa invariants, Manuscr. Math., Volume 148 (2015), pp. 521-533 | DOI | MR | Zbl

[13] Michel Van den Bergh Three-dimensional flops and noncommutative rings, Duke Math. J., Volume 122 (2004) no. 3, pp. 423-455 | MR | Zbl

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