On the existence of Ulrich vector bundles on some irregular surfaces

Lopez, Angelo

doi:10.1090/proc/15278

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
MathSciNet review: 4172582
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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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