Koszul homology and syzygies of Veronese subalgebras
By W. Bruns, Aldo Conca, Tim Römer. 2009
54 citations recorded by the source corpus.
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 Green–Lazarsfeld 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 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 $${c\gg 0}$$.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/aa1bdbe5535538c53ec2fc42ae69593acac8469f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- L. Ein
- R. Lazarsfeld
- M. Mustaţă
- Robert J. Berman
- Morihiko Saito
- Mattias Jonsson
- Igor Dolgachev
- Karl Schwede
In Geometry and Topology
- L. Ein
- R. Lazarsfeld
- M. Mustaţă
- Tommaso de Fernex
- Mattias Jonsson
- Robert J. Berman
- Karl Schwede
- Morihiko Saito
Citations in the corpus
- Koszul Algebras and Regularity (2012, unknown): “The material we present is taken from various sources (see [3, 8, 10–12, 16, 24–27, 32, 42, 58]).”
- Asymptotic syzygies of algebraic varieties (2011, background): “d)|, so that we are studying the asymptotic behavior of the syzygies of the d-fold Veronese embedding of Pn. These Veronese syzygies have been the focus of a great deal of attention, e.g. [23], [25], [4], [5]. We establish an effective result that at least in some cases is best-possible. Theorem B. F”