Graded derivation modules and algebraic free divisors
The main goal of the article is to provide new characterizations of what it means for certain homogeneous forms to be free divisors (in the sense of [\textit{K. Saito}, J. Fac. Sci., Univ. Tokyo, Sect. I A 27, 265--291 (1980; Zbl 0496.32007)]). These characterizations are given in terms of the minimal number of generators of particular modules of derivations associated to the hypersurface ring defined by the form. Along the way, the author investigates several invariants of the modules of derivations of such hypersurface rings, such as the Castelnuovo-Mumford regularity and the Hilbert function. The case of a cuspidal projective plane cubic is examined in detail. A characterization of \(linear\) free divisors, as defined in [\textit{R.-O. Buchweitz} and \textit{D. Mond}, Lond. Math. Soc. Lect. Note Ser. 324, 41--77 (2006; Zbl 1101.14013)], involving the Ulrichness of a certain ideal, is also established.
scientific article; zbMATH DE number 6476977
scientific article