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Products of homogeneous forms

By E Ballico

Abstract

AbstractHere we give a geometric proof of the following result. Let K be an algebraically closed field. Fix an integer s⩾1 and positive integers ni and di, 1⩽i⩽s. Set mi=min{ni,di+1}. For 1⩽i⩽s and 1⩽j⩽ni, take general homogeneous forms Fij∈K[x,y] with deg(Fij)=di. Let Ii⊂K[x,y] be the homogeneous ideal generated by the forms Fij, for 1⩽j⩽ni. Let d≔∑i=1sdi and denote by (I1⋯Is)d be the degree d part of the homogeneous ideal I1⋯Is. Thendim(I1⋯Is)d=min∏i=1smi,d+1

Publisher: Elsevier Science B.V.
Year: 2002
DOI identifier: 10.1016/S0022-4049(01)00164-5
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