J 2011

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

HARRIS, Adam a Martin KOLÁŘ

Základní 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

Štítky

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