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

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

2001-03-02

arxiv.org/abs/math/0103010v1

Rev. Roumaine Math. Pures Appl. 47 (2002), no. 2, 211-222

Mathematics

Algebraic Geometry

9 pages

Scientific paper

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.

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