SHARP UPPER BOUND FOR THE REGULARITY OF ZERO-SCHEMES OF DOUBLE POINTS IN

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.