On affine complete intersections with isolated singularities

[摘要] We consider an algebraic set W in R-n, defined by the vanishing of k (0 < k < n) polynomials, to which we associate a polynomial algebra A(R). Assuming that A(R) is a finite dimensional vector space over R, we prove that the complexification W-C of W is a complete intersection of codimension k with at most isolated singularities and that chi (W) + Sigma (s)(t=1)mu (i) equivalent to dim(R) A(R) mod 2, where the mu (i) are the Milnor numbers of the singularities lying in W. We also obtain a formula for the semi-characteristic of the link at infinity of TV. For the special cases of curves and odd-dimensional hypersurfaces, we show how to refine our formulas. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-10-24

[效力级别]  Proceedings Paper