Elliptic curves, ACM bundles and Ulrich bundles on prime Fano threefolds
Ciro Ciliberto, Flaminio Flamini, Andreas Leopold Knutsen

TL;DR
This paper studies elliptic curves, ACM bundles, and Ulrich bundles on prime Fano threefolds, establishing their existence, dimension, and properties, and completing the classification of rank-two ACM bundles on these threefolds.
Contribution
It proves the existence and describes the moduli spaces of elliptic curves, ACM bundles, and Ulrich bundles on prime Fano threefolds, completing their classification and showing the wildness of Ulrich bundles.
Findings
Hilbert schemes of elliptic curves are nonempty with expected dimension
Moduli spaces of rank-two ACM bundles are nonempty and reduced in general
Ulrich bundles of all ranks exist with specified properties and are abundant
Abstract
Let be any smooth prime Fano threefold of degree in , with . We prove that for any integer satisfying the Hilbert scheme parametrizing smooth irreducible elliptic curves of degree in is nonempty and has a component of dimension , which is furthermore reduced except for the case when and is contained in a singular quadric. Consequently, we deduce that the moduli space of rank--two slope--stable bundles on such that , and is nonempty and has a component of dimension , which is furthermore reduced except for the case when and is contained in a singular quadric. This completes the…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Vietnamese History and Culture Studies · North African History and Literature
