Koszul homology and syzygies of Veronese subalgebras

Autor(en): Bruns, Winfried 
Conca, Aldo
Roemer, Tim 
Stichwörter: Mathematics; REGULARITY
Erscheinungsdatum: 2011
Herausgeber: SPRINGER HEIDELBERG
Journal: MATHEMATISCHE ANNALEN
Volumen: 351
Ausgabe: 4
Startseite: 761
Seitenende: 779
Zusammenfassung: 
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 a parts per thousand currency sign 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 a parts per thousand yen c 1. The same conclusion also holds for an arbitrary standard graded algebra, provided c >> 0.
ISSN: 00255831
DOI: 10.1007/s00208-010-0616-1

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