Identifying limits of ideals of points in the case of projective space. (English) Zbl 1509.14011
Summary: We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective space. In the case of projective plane, we give a sufficient condition for an ideal to be in the closure of the locus of radical ideals. For projective space of arbitrary dimension we present a necessary condition. The paper is motivated by the border apolarity lemma which connects such multigraded Hilbert schemes with the theory of ranks of polynomials.
MSC:
| 14C05 | Parametrization (Chow and Hilbert schemes) |
| 14N07 | Secant varieties, tensor rank, varieties of sums of powers |
Software:
Macaulay2References:
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