Koszul homology and syzygies of Veronese subalgebras

Winfried Bruns, Aldo Conca, Tim Roemer
Arxiv ID: 0902.2431Last updated: 5/18/2021
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 less or equal to 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 K) the c-th Veronese subring of a polynomial ring has Green-Lazarsfeld index greater or equal to c+1. The same conclusion also holds for an arbitrary standard graded algebra, provided c is sufficiently large.

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