A remarkable moduli space of rank 6 vector bundles related to cubic surfaces
| dc.creator | Catanese, Fabrizio | |
| dc.creator | Tonoli, Fabio | |
| dc.date | 2007-05-15 | |
| dc.date.accessioned | 2026-07-07T08:01:41Z | |
| dc.date.available | 2026-07-07T08:01:41Z | |
| dc.description | We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first recall how these bundles are related to the construction of sextic nodal surfaces in $\PP^3$ having an even set of 56 nodes (cf. \cite{CaTo}). We prove that there is an open set, corresponding to the simple bundles with minimal cohomology, which is irreducible of dimension 19 and bimeromorphic to an open set $\fA^0$ of the G.I.T. quotient space of the projective space $\fB:=\{B\in \PP(U^\vee\otimes W\otimes V^\vee)\}$ of triple tensors of type $(3,3,4)$ by the natural action of $SL(W)\times SL(U)$. We give several constructions for these bundles, which relate them to cubic surfaces in 3-space $\PP^3$ and to cubic surfaces in the dual space $(\PP^3)^{\vee}$. One of these constructions, suggested by Igor Dolgachev, generalizes to other types of tensors. Moreover, we relate the socalled {\em cross-product involution} for $(3,3,4)$-tensors, introduced in \cite{CaTo}, with the Schur quadric associated to a cubic surface in $\PP^3$ and study further properties of this involution. | |
| dc.description | 39 pages, to appear in "Vector bundles and low codimensional subvarieties: state of the art and recent developments" in the Series "Quaderni di Matematica" della Seconda Universita' di Napoli | |
| dc.identifier | https://arxiv.org/abs/0705.2184 | |
| dc.identifier | http://arxiv.org/abs/0705.2184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128990 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M99; 14N25; 14F05; 14J60; 14Q10; 13D02 | |
| dc.title | A remarkable moduli space of rank 6 vector bundles related to cubic surfaces | |
| dc.type | text |