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Ulrich bundles on smooth projective varieties of minimal degree


Authors: M. Aprodu, S. Huh, F. Malaspina and J. Pons-Llopis
Journal: Proc. Amer. Math. Soc. 147 (2019), 5117-5129
MSC (2010): Primary 14J60; Secondary 13C14, 14F05
DOI: https://doi.org/10.1090/proc/14640
Published electronically: June 14, 2019
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Abstract: We classify Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.


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Additional Information

M. Aprodu
Affiliation: Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei Street, 010014 Bucharest, Romania; and “Simion Stoilow” Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700 Bucharest, Romania
Email: marian.aprodu@fmi.unibuc.ro, marian.aprodu@imar.ro

S. Huh
Affiliation: Sungkyunkwan University, Suwon 440-746, Republic of Korea
Email: sukmoonh@skku.edu

F. Malaspina
Affiliation: Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: francesco.malaspina@polito.it

J. Pons-Llopis
Affiliation: Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Email: juan.ponsllopis@polito.it

DOI: https://doi.org/10.1090/proc/14640
Keywords: Ulrich bundle, rational normal scroll, Beilinson spectral theorem
Received by editor(s): January 8, 2018
Received by editor(s) in revised form: March 22, 2019, and March 25, 2019
Published electronically: June 14, 2019
Additional Notes: The first author was partly supported by a grant from the Ministery of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0030, within PNCDI III
The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1C1A6004285 and No. 2016R1A5A1008055).
The third author was supported by the framework of PRIN 2010/11 “Geometria delle varietà algebriche”, cofinanced by MIUR and GNSAGA of INDAM (Italy)
The fourth author was supported by an FY2015 JSPS Postdoctoral Fellowship
Communicated by: Lev Borisov
Article copyright: © Copyright 2019 American Mathematical Society