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@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 a Martin KOLÁŘ. On infinitesimal deformations of the regular part of a complex cone singularity. \textit{Kyushu Journal of Mathematics}. Fukioka (Japan): Kyushu University, 2011, roč.~65, č.~1, s.~25-38. ISSN~1340-6116. Dostupné z: https://dx.doi.org/10.2206/kyushujm.65.25.
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