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arXiv · 0910.3569

Bipolynomial Hilbert functions

E. Carlini·M. V. Catalisano·A. V. Geramita
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Abstract

Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively, the Hilbert function and the Hilbert polynomial of X. We say that X has bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every non-negative integer d. We show that if X consists of a plane and generic lines, then X has bipolynomial Hilbert function. We also conjecture that generic configurations of non-intersecting linear spaces have bipolynomial Hilbert function.

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E. Carlini, M. V. Catalisano, A. V. Geramita. 2009-10-19. Bipolynomial Hilbert functions. https://arxiv.org/abs/0910.3569

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