ACM vector bundles on prime Fano threefolds and complete intersection Calabi Yau threefolds

Abstract

In this paper we derive a list of all the possible indecomposable normalized rank--two vector bundles without intermediate cohomology on the prime Fano threefolds and on the complete intersection Calabi Yau threefolds, say $V$, of Picard number $\rho =1$. For any such bundle $\E$, if it exists, we find the projective invariants of the curves $C\subset V$ which are the zero-locus of general global sections of $\E$. In turn, a curve $C\subset V$ with such invariants is a section of a bundle $\E$ from our lists. This way we reduce the problem for existence of such bundles on $V$ to the problem for existence of curves with prescribed properties contained in $V$. In part of the cases in our lists the existence of such curves on the general $V$ is known, and we state the question about the existence on the general $V$ of any type of curves from the lists.

9 pages

References in corpus (2)

• The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold
• A splitting criterion for rank 2 vector bundles on hypersurfaces in P^4

Cited by in corpus (5)

• On holomorphic distributions on Fano threefolds
• Curves and vector bundles on quartic threefolds
• Ulrich bundles on intersections of two 4-dimensional quadrics
• Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
• Moduli spaces of rank 2 ACM bundles on prime Fano threefolds