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Bounds for Betti Numbers

✍ Scribed by Tim Römer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
144 KB
Volume
249
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 kth syzygy module over the polynomial ring. If in addition the module is ‫ޚ‬ 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 Ž .

a fixed number of generators.

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