Graded Betti Numbers of the Logarithmic Derivation Module

Details Graded Betti Numbers of the Logarithmic Derivation Module Graded Betti Numbers of the Logarithmic Derivation Module

2009-04-22

arxiv.org/abs/0904.3465v1

Mathematics

Commutative Algebra

Scientific paper

Let $Q\in \K[x_1,...,x_n] = S$ be a homogeneous polynomial of degree $d$. The freeness of the logarithmic derivation module, $D(Q)$, and of its natural generalizations, has been widely studied. In the free case, $D(Q) \simeq \bigoplus_{i=1}^n S(-d_i)$ where the $d_i$'s are the exponents of the module; and as a direct consequence of the Saito-Ziegler criterion, the formula $d = \sum_i d_i$ holds. In this paper 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.

Affiliated with

Also associated with

No associations

Rating

Graded Betti Numbers of the Logarithmic Derivation Module does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Graded Betti Numbers of the Logarithmic Derivation Module, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graded Betti Numbers of the Logarithmic Derivation Module will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-275189