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On the existence of Ulrich vector bundles on some irregular surfaces


Author: Angelo Felice Lopez
Journal: Proc. Amer. Math. Soc. 149 (2021), 13-26
MSC (2010): Primary 14J60; Secondary 14J27, 14J29
DOI: https://doi.org/10.1090/proc/15278
Published electronically: October 16, 2020
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Abstract: We establish the existence of rank two Ulrich vector bundles on surfaces that are either of maximal Albanese dimension or with irregularity $ 1$, under many embeddings. In particular, we get the first known examples of Ulrich vector bundles on irregular surfaces of general type. Another consequence is that every surface such that either $ q \le 1$ or $ q \ge 2$ and its minimal model has rank one, carries a simple rank two Ulrich vector bundle.


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Additional Information

Angelo Felice Lopez
Affiliation: Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy
Email: lopez@mat.uniroma3.it

DOI: https://doi.org/10.1090/proc/15278
Received by editor(s): January 31, 2019
Received by editor(s) in revised form: April 10, 2020
Published electronically: October 16, 2020
Additional Notes: This research was partially supported by PRIN “Geometria delle varietà algebriche” and GNSAGA-INdAM
Communicated by: Alexander Braverman
Article copyright: © Copyright 2020 American Mathematical Society