Mixed multiplicities, Hilbert polynomials and homaloidal surfaces. Issue 5 (12th September 2016) - Dimca, Alexandru; Sticlaru, Gabriel
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.