Bounds for Betti numbers

Details Bounds for Betti numbers Bounds for Betti numbers

2000-08-04

arxiv.org/abs/math/0008041v2

J. Algebra 249, No. 1, 20-37 (2002)

Mathematics

Commutative Algebra

15 pages

Scientific paper

In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded $k$-th syzygy module over the polynomial ring. If in addition the module is $\mathbb{Z}^n$-graded we show that the conjecture holds in full generality. Furthermore, we give lower and upper bounds for the graded Betti numbers of graded ideals with a linear resolution and a fixed number of generators.

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