The pinched Veronese is Koszul
| dc.creator | Caviglia, Giulio | |
| dc.date | 2006-02-22 | |
| dc.date.accessioned | 2026-07-07T07:03:41Z | |
| dc.date.available | 2026-07-07T07:03:41Z | |
| dc.description | In this paper we prove that the coordinate ring of the pinched Veronese (i.e $k[X^3,X^2Y,XY^2,Y^3,X^2Z,Y^2Z,XZ^2,YZ^2,Z^3]\subset k[X,Y,Z]$) is Koszul. The strategy of the proof is the following: we can consider a presentation $S/I$ where $S=k[X_1,...,X_9]$. Using a distinguished weight $ω$, it's enough to show that $S/in_ωI$ is Koszul. We write $in_ωI$ as $J+H$ where $J$ is generated by a Gröbner basis of quadrics. Finally, we present an extension of the notion of Koszul filtration and we use it to show that $(J+H)/J$ has a linear free resolution over $S/J.$ This implies the Koszulness of $S/I.$ | |
| dc.description | 8 Pages | |
| dc.identifier | https://arxiv.org/abs/math/0602487 | |
| dc.identifier | http://arxiv.org/abs/math/0602487 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109065 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 16S37; 13P10 | |
| dc.title | The pinched Veronese is Koszul | |
| dc.type | text |