On infinitesimal deformations of the regular part of a complex
cone singularity

J 2011

On infinitesimal deformations of the regular part of a complex cone singularity

HARRIS, Adam and Martin KOLÁŘ

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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Japan

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

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

Abstract

V originále

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

Citovat

HARRIS, Adam and Martin KOLÁŘ. On infinitesimal deformations of the regular part of a complex cone singularity. 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.

@article{978538,
   author = {Harris, Adam and Kolář, Martin},
   article_location = {Fukioka (Japan)},
   article_number = {1},
   doi = {http://dx.doi.org/10.2206/kyushujm.65.25},
   keywords = {complex deformations; cone singularities; Kahler metric},
   language = {eng},
   issn = {1340-6116},
   journal = {Kyushu Journal of Mathematics},
   title = {On infinitesimal deformations of the regular part of a complex cone singularity},
   url = {http://www.jstage.jst.go.jp/article/kyushujm/65/1/25/_pdf},
   volume = {65},
   year = {2011}
}

TY  - JOUR
ID  - 978538
AU  - Harris, Adam - Kolář, Martin
PY  - 2011
TI  - On infinitesimal deformations of the regular part of a complex cone singularity
JF  - Kyushu Journal of Mathematics
VL  - 65
IS  - 1
SP  - 25-38
EP  - 25-38
PB  - Kyushu University
SN  - 13406116
KW  - complex deformations
KW  - cone singularities
KW  - Kahler metric
UR  - http://www.jstage.jst.go.jp/article/kyushujm/65/1/25/_pdf
L2  - http://www.jstage.jst.go.jp/article/kyushujm/65/1/25/_pdf
N2  - 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
ER  -

HARRIS, Adam and Martin KOLÁŘ. On infinitesimal deformations of the regular part of a complex cone singularity. \textit{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.

Detailed Information on Publication Record