ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 32G Miyajima, Kimio, Kagoshima University, Japan CR construction of the semi-universal family of normal isolated singularities. It is a natural idea to construct the semi-universal family of normal isolated singularities in terms of deformations of CR-structures on the boundary; what is called the Kuranishi program. The works of T. Akahori, R. O. Buchweitz-J. J. Millson and K. Miyajima solved it under the assumptions dim_{C}V ≥ 4 and depthO_{V} ≥ 3. In this talk, I will accomplish the Kuranishi program without the above assumptions, by considering stably embeddable deformations of CR structures introduced by J. Bland and C. L. Epstein in the surface singularity case [J. Alg. Geom. 5 (1996), 277–368]. References: K. Miyajima, CR-construction of the flat deformations of normal isolated singularities, preprint 1998. ——, Deformation theory of CRstructures and its application to deformations of isolated singularities II, Advanced Studies in Pure Mathematics 25, Kinokuniya, 1997, 247–275.