Rank 4 vector bundles on the quintic threefold
| dc.creator | Madonna, C. | |
| dc.date | 2001-10-23 | |
| dc.date | 2005-05-02 | |
| dc.date.accessioned | 2026-07-07T04:44:02Z | |
| dc.date.available | 2026-07-07T04:44:02Z | |
| dc.description | By the results of the author and Chiantini in Math.AG/0110102, on a general quintic threefold $X \subset {\mathbf P}^4$ the minimum integer $p$ for which there exists a positive dimensional family of irreducible rank $p$ vector bundles on $X$ without intermediate cohomology is at least three. In this paper we show that $p \leq 4$, by constructing series of positive dimensional families of rank 4 vector bundles on $X$ without intermediate cohomology. The general member of such family is an indecomposable bundle from the extension class $Ext^1(E,F)$, for a suitable choice of the rank 2 ACM bundles $E$ and $F$ on $X$. The existence of such bundles of rank $p = 3$ remains under question. | |
| dc.description | v2: 8 pages. Title changed. One wrong example is removed. More explicit examples are given - v3: typos corrected according to referees suggestions - v.4 final version, to appear on Central European Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0110259 | |
| dc.identifier | http://arxiv.org/abs/math/0110259 | |
| dc.identifier | CEJM 3(3) 2005, 404-411 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62475 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F05 | |
| dc.title | Rank 4 vector bundles on the quintic threefold | |
| dc.type | text |