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Mixed multiplicities, Hilbert polynomials and homaloidal surfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Sep 2016Embargo end date: 01 Jan 2015Publisher:WileyJournal:Mathematische Nachrichten, volume 290, pages 785-793 (issn: 0025-584X,

Authors: Alexandru Dimca; Gabriel Sticlaru;

doi: 10.1002/mana.201600205 , 10.48550/arxiv.1507.08543

arXiv: http://arxiv.org/abs/1507.08543

Mixed multiplicities, Hilbert polynomials and homaloidal surfaces

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Abstract

We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface $V$: the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when $V$ is free. As a byproduct, we obtain explicit equations for some of the homaloidal surfaces in the projective 3-dimensional space constructed by C. Ciliberto, F. Russo and A. Simis.

v5: the following key reference added: N. V. Trung, Positivity of mixed multiplicities, Math. Ann. 319 (2001), 33-63

Related Organizations

Centre national de la recherche scientifique
France
Ovidius University
Romania
Université Côte d'Azur
France
French National Centre for Scientific Research
France

Keywords

Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)

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