Graded Betti Numbers of the Logarithmic Derivation Module

Marco Buzunariz, Miguel Angel ; Martin-Morales, Jorge

Resumen: Let Q ¿ x1 xn = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, DQ, and of its natural generalizations has been widely studied. In the free case, DQ n i=1 S-di, where the di’s are the exponents of the module; and as a direct consequence of the Saito–Ziegler criterion, the formula d = i di holds. In this article, we give a generalization of this formula in the non-free case. Moreover, we show that an equivalent formula is also true in the quasi-homogeneous case, and show to what extent it can be generalized for arbitrary polynomials.

Idioma: Inglés

DOI: 10.1080/00927870903366918

Año: 2011

Publicado en: COMMUNICATIONS IN ALGEBRA 38, 11 (2011), 4348-4361
ISSN: 0092-7872

Factor impacto JCR: 0.347 (2011)

Categ. JCR: MATHEMATICS rank: 235 / 289 = 0.813 (2011) - Q4 - T3

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15

Tipo y forma: Article (PostPrint)