Koszul Homology and Syzygies of Veronese Subalgebras
نویسندگان
چکیده
A graded K-algebra R has property Np if it is generated in degree 1, has relations in degree 2 and the syzygies of order ≤ p on the relations are linear. The GreenLazarsfeld index of R is the largest p such that it satisfies the property Np. Our main results assert that (under a mild assumption on the base field) the c-th 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 ≫ 0.
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