Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds
Matej Filip
TL;DR
This paper classifies indecomposable rank 2 ACM bundles on complete intersection Calabi-Yau threefolds, revealing new geometric properties and proving the existence of higher rank bundles on specific CICYs.
Contribution
It provides a classification of rank 2 ACM bundles on CICY threefolds and establishes the existence of higher rank bundles, with new geometric insights derived from free resolutions.
Findings
Classification of indecomposable rank 2 ACM bundles on CICY threefolds
New geometric properties of associated curves
Existence of higher rank bundles on (2,4) CICY
Abstract
The aim of this paper is to classify indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on compete intersection Calabi-Yau (CICY) threefolds and prove the existence of some of them. New geometric properties of the curves corresponding to rank 2 ACM bundles (by Serre correspondence) are obtained. These follow from minimal free resolutions of curves in suitably chosen fourfolds (containing Calabi-Yau threefolds as hypersurfaces). Also the existence of an indecomposable vector bundle of higher rank on a CICY threefold of type (2,4) is proved.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Biological Activity of Diterpenoids and Biflavonoids