HARRIS, Adam and Martin KOLÁŘ. On infinitesimal deformations of the regular part of a complex cone singularity. Online. Kyushu Journal of Mathematics. Fukioka (Japan): Kyushu University, 2011, vol. 65, No 1, p. 25-38. ISSN 1340-6116. Available from: https://dx.doi.org/10.2206/kyushujm.65.25. [citováno 2024-04-24]
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Basic information
Original name On infinitesimal deformations of the regular part of a complex cone singularity
Authors HARRIS, Adam (36 Australia) and Martin KOLÁŘ (203 Czech Republic, guarantor, belonging to the institution)
Edition Kyushu Journal of Mathematics, Fukioka (Japan), Kyushu University, 2011, 1340-6116.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Japan
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 0.366
RIV identification code RIV/00216224:14310/11:00056738
Organization unit Faculty of Science
Doi http://dx.doi.org/10.2206/kyushujm.65.25
UT WoS 000290462800003
Keywords (in Czech) komplexní deformace; kuželová singularita; Kahlerova metrika
Keywords in English complex deformations; cone singularities; Kahler metric
Tags AKR, rivok, ZR
Tags International impact, Reviewed
Changed by Changed by: Ing. Zdeňka Rašková, učo 140529. Changed: 20/4/2012 11:12.
Abstract
This article follows recent work of Miyajima on the complex-analytic approach to deformations of the regular part (i.e. the punctured smooth neighbourhood) of isolated singularities. Attention has previously focused on stably-embeddable infinitesimal deformations as those which correspond to standard algebraic deformations of the germ of a variety, and which also lead to convergent series solutions of the Kodaira-Spencer integrability equation. The emphasis of the present paper, however, is on the subspaces Z(0) of first cohomology classes containing infinitesimal deformations with vanishing Kodaira- Spencer bracket, and W(0), consisting more broadly of deformations for which the bracket represents the trivial second cohomology class. Deformations representing classes in Z(0) are automatically integrable, regardless of their analytic behaviour near the singular point. Classes in W(0) are those for which only the first formal obstruction to integrability is overcome. After some preliminary results on cohomology, the main theorem of this paper gives a partial description of the analytic geometry of Z(0) and W(0) for affine cones of arbitrary
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