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Koszul homology and syzygies of Veronese subalgebras

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A graded K-algebra R has property N p if it is generated in degree 1, has relations in degree 2 and the syzygies of order ≤ p on the relations are linear. The Green–Lazarsfeld index of R is the largest p such that it satisfies the property N p . Our main results assert that (under a mild assumption on the base field) the cth Veronese subring of a polynomial ring has Green–Lazarsfeld index ≥ c + 1. The same conclusion also holds for an arbitrary standard graded algebra, provided \({c\gg 0}\).

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Authors and Affiliations

  1. Institut für Mathematik, Universität Osnabrück, 49069, Osnabrück, Germany

    Winfried Bruns & Tim Römer

  2. Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, 16146, Genoa, Italy

    Aldo Conca

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  1. Winfried Bruns
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  2. Aldo Conca
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  3. Tim Römer
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Correspondence to Winfried Bruns.

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To Jürgen Herzog, friend and teacher.

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Bruns, W., Conca, A. & Römer, T. Koszul homology and syzygies of Veronese subalgebras. Math. Ann. 351, 761–779 (2011). https://doi.org/10.1007/s00208-010-0616-1

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