The colorful Helly theorem and colorful resolutions of ideals

Details The colorful Helly theorem and colorful resolutions of ideals The colorful Helly theorem and colorful resolutions of ideals

2008-09-19

arxiv.org/abs/0809.3366v2

Journal of Pure and Applied Algebra 215, (2011), no. 6, p. 1255-1262

Mathematics

Commutative Algebra

13 pages, minor changes

Scientific paper

10.1016/j.jpaa.2010.08.009

We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum may be viewed as different versions of the same phenomenon. Using this correspondence we show how the colorful Helly theorem of I.Barany and its generalizations by G.Kalai and R.Meshulam translates to the algebraic side. Our main results are algebraic generalizations of these translations, which in particular gives a syzygetic version of Hellys theorem.

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