Mathematics – Algebraic Geometry
Scientific paper
2001-10-23
CEJM 3(3) 2005, 404-411
Mathematics
Algebraic Geometry
v2: 8 pages. Title changed. One wrong example is removed. More explicit examples are given - v3: typos corrected according to
Scientific paper
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.
No associations
LandOfFree
Rank 4 vector bundles on the quintic threefold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Rank 4 vector bundles on the quintic threefold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rank 4 vector bundles on the quintic threefold will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-651151