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Mixed multiplicities, Hilbert polynomials and homaloidal surfaces
Author(s) -
Dimca Alexandru,
Sticlaru Gabriel
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600205
Subject(s) - mathematics , hypersurface , jacobian matrix and determinant , sequence (biology) , ideal (ethics) , polynomial , pure mathematics , hilbert space , projective space , exponent , complex projective space , projective test , mathematical analysis , philosophy , linguistics , genetics , epistemology , biology
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.