Mixed multiplicities, Hilbert polynomials and homaloidal surfaces. Issue 5 (12th September 2016)

• Record Type: Journal Article
• Authors: Dimca, Alexandru; Sticlaru, Gabriel
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 5/6(2017)
• Page Start: 785
• Page End: 793
• Publication Date: 2016-09-12
• Subjects: Mixed multiplicities -- Jacobian ideal -- Hilbert polynomial -- homaloidal surfaces -- Primary: 14E07 -- Secondary: 13D40 -- 14J70 -- 32S22; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201600205
• Languages: English
• ISSNs: 0025-584X

Abstract

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.