ON INFINITESIMAL DEFORMATIONS OF THE REGULAR PART OF A COMPLEX CONE SINGULARITY

概要

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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 dimension.
Faculty of Mathematics, Kyushu Universityの論文
2011-03-00