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The colorful Helly theorem and colorful resolutions of ideals

Research paper by Gunnar Floystad

Indexed on: 10 Aug '10Published on: 10 Aug '10Published in: Mathematics - Commutative Algebra



Abstract

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.