ABSTRACT
We will give a sharp bound for the regularity of the subscheme in defined by forms which have singularities at a given set of points.
ACKNOWLEDGMENTS
The author is greatly indebted to Prof. N.V. Trung for his guidance and to the Institute of Mathematics (Hanoi) for hospitality during the preparation of the paper. The author would like to thank L.T. Hoa for helpful discussions. Thanks are also due to the referee for helpful suggestions.