会場

埼玉大学理学部1号館3階 基礎数理演習室 （このページの理学部と書いてある建物が1号館です）

講演者

福井 敏純 氏 (埼玉大学)

タイトル

Lipschitz property v.s. blow-analyticity for semi algebraic homeomorphisms

アブストラクト

We say a map is blow-analytic if there is a composition of blow ups with nonsingular centers of the source so that the composition is analytic. We are going to discuss several relations between Lipschitz properties and blow-analyticity for semi-algebraic homeomorphisms $f:R^n,0 ?to R^n,0$. The goal is to show the equivalence of the following two conditions:
1) $f$ is blow-analytic and $f^{-1}$ is Lipschitz
2) $f^{-1}$ is blow-analytic and $f$ is Lipschitz
This is a joint work with Krzysztof Kurdyka and Adam Parusinski.

講演者

A.G.Aleksandrov 氏 (Moscow)

タイトル

Index of vector fields on singular varieties

アブストラクト

We discuss simple methods of computation of the local topological index of vector fields on singular varieties. Our approach is mainly based on the notion of homological index originated in a paper by X.G\’omez-Mont (1998), on earlier results by the author published in 1983-1990, and on simple properties of holomorphic and regular meromorphic differential forms; it can be applied in different situations depending on concrete types of varieties. Thus, we describe how to compute the index in the case of Cohen-Macaulay curves, complete intersections and toric varieties by elementary calculations. For quasihomogeneous complete intersections with isolated singularities an explicit formula for the index is obtained; in this case the computation of the homological index is reduced to the use of Newton’s binomial formula only.