Ulrich bundles on ruled surfaces

In this short note, we study the existence problem for Ulrich bundles on polarized ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient αof the minimal section in the numerical class of the polarizat...

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Bibliographic Details
Authors: Aprodu, Marian, Costa Farràs, Laura, Miró-Roig, Rosa M. (Rosa Maria)
Format: article
Status:Versión aceptada para publicación
Publication Date:2018
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/120550
Online Access:https://hdl.handle.net/2445/120550
Access Level:Open access
Keyword:Superfícies algebraiques
Geometria algebraica
Algebraic surfaces
Algebraic geometry
Description
Summary:In this short note, we study the existence problem for Ulrich bundles on polarized ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient αof the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles.