2011
On infinitesimal deformations of the regular part of a complex cone singularity
HARRIS, Adam a Martin KOLÁŘZákladní údaje
Originální název
On infinitesimal deformations of the regular part of a complex cone singularity
Autoři
HARRIS, Adam (36 Austrálie) a Martin KOLÁŘ (203 Česká republika, garant, domácí)
Vydání
Kyushu Journal of Mathematics, Fukioka (Japan), Kyushu University, 2011, 1340-6116
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10101 Pure mathematics
Stát vydavatele
Japonsko
Utajení
není předmětem státního či obchodního tajemství
Odkazy
Impakt faktor
Impact factor: 0.366
Kód RIV
RIV/00216224:14310/11:00056738
Organizační jednotka
Přírodovědecká fakulta
UT WoS
000290462800003
Klíčová slova česky
komplexní deformace; kuželová singularita; Kahlerova metrika
Klíčová slova anglicky
complex deformations; cone singularities; Kahler metric
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 20. 4. 2012 11:12, Ing. Zdeňka Rašková
Anotace
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