Abstract
It is a longstanding problem to determine whether the d-uple Veronese embedding of \({\mathbb {P}}^k\) supports a rank r Ulrich bundle. In this short note, we explicitly determine the integers d and r such that rank r Ulrich bundles on \({\mathbb {P}}^2\) for the Veronese embedding \({\mathcal {O}}(d)\) exist and, in particular, we solve Conjecture A.1 in Coskun and Genc (Proc Am Math Soc 145:4687–4701, 2017).
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Acknowledgements
The authors dedicate this note to Antonio Campillo for his 65th birthday in recognition to his contributions to Algebraic Geometry in Spain. The authors are partially supported by MTM2016-78623-P.
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Costa, L., Miró-Roig, R.M. (2018). Ulrich Bundles on Veronese Surfaces. In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_14
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DOI: https://doi.org/10.1007/978-3-319-96827-8_14
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