Mixed multiplicities, Hilbert polynomials and homaloidal surfaces
Algebraic Geometry
2017-08-30 v5 Commutative Algebra
Abstract
We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface : the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when 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.
Cite
@article{arxiv.1507.08543,
title = {Mixed multiplicities, Hilbert polynomials and homaloidal surfaces},
author = {Alexandru Dimca and Gabriel Sticlaru},
journal= {arXiv preprint arXiv:1507.08543},
year = {2017}
}
Comments
v5: the following key reference added: N. V. Trung, Positivity of mixed multiplicities, Math. Ann. 319 (2001), 33-63