Comptes Rendus
no. S1
Article de recherche - Géométrie algébrique
Deformations over non-commutative base
[Déformations sur une base non-commutative]
Yujiro Kawamata1
1 Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
Comptes Rendus. Mathématique, Complex algebraic geometry, in memory of Jean-Pierre Demailly, Volume 362 (2024) no. S1, pp. 159-169.

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 T1 and T2.

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 T1 et T2.

Reçu le :
Accepté le :
Publié le :
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 
@article{CRMATH_2024__362_S1_159_0,
     author = {Yujiro Kawamata},
     title = {Deformations over non-commutative base},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {159--169},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {S1},
     year = {2024},
     doi = {10.5802/crmath.622},
     language = {en},
}
TY  - JOUR
AU  - Yujiro Kawamata
TI  - Deformations over non-commutative base
JO  - Comptes Rendus. Mathématique
PY  - 2024
SP  - 159
EP  - 169
VL  - 362
IS  - S1
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.622
LA  - en
ID  - CRMATH_2024__362_S1_159_0
ER  - 
%0 Journal Article
%A Yujiro Kawamata
%T Deformations over non-commutative base
%J Comptes Rendus. Mathématique
%D 2024
%P 159-169
%V 362
%N S1
%I Académie des sciences, Paris
%R 10.5802/crmath.622
%G en
%F CRMATH_2024__362_S1_159_0
Yujiro Kawamata. Deformations over non-commutative base. Comptes Rendus. Mathématique, Complex algebraic geometry, in memory of Jean-Pierre Demailly, 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

Cité par Sources :

Commentaires - Politique