The colorful Helly theorem and colorful resolutions of ideals |
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Authors: | Gunnar Fløystad |
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Institution: | Department of Mathematics, Johs. Brunsgt. 12, 5008 Bergen, Norway |
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Abstract: | We demonstrate that the topological Helly theorem and the algebraic Auslander-Buchsbaum theorem 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 translate to the algebraic side. Our main results are algebraic generalizations of these translations, which in particular give a syzygetic version of Helly’s theorem. |
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Keywords: | Primary 13D02 Secondary 13F55 05E99 |
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