Inverse Systems of Zero-dimensional Schemes in Pⁿ

2011/07/01 by Cho, Young Hyun, Iarrobino, Anthony
#13D40 #13H10 #13N10 #14C05 (Secondary) #14N05 (Primary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1107.0094

Abstract

The authors construct the global Macaulay inverse system for a zero-dimensional subscheme Z of projective n-space Pⁿ, from the local inverse systems of the irreducible components of Z. They show that when Z is locally Gorenstein a generic homogeneous form F of degree d apolar to Z determines Z when d is larger than an invariant b(Z). They also show that a natural upper bound for the Hiilbert function of Gorenstein Artin quotient of the coordinate ring is achieved for large socle degree. They show the uniqueness of generalized additive decompositions of a homogeneous form F into powers of linear forms, under suitable hypotheses. They include many examples.

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