Ulrich bundles on cyclic coverings of projective spaces

2024/08/20 by A. J. Parameswaran, Jagadish Pine, Parameswaran, A. J. +1 · 3 citations
#math.AG

paper · pdf · doi:10.48550/arxiv.2408.10837

Abstract

We prove the existence of Ulrich bundles on cyclic coverings of ℙⁿ of arbitrary degree d. Given a relatively Ulrich bundle on a complete intersection subvariety, we construct a relatively Ulrich bundle on the ambient variety. As an application, we prove that there exists a rank d Ulrich bundle on a generic cyclic covering of ℙ² of degree d, provided that the degree d ⋅ k of the branch divisor is even. When d ⋅ k is odd, we also provide an estimation of the rank of the Ulrich bundle on a generic cyclic covering of ℙ².

Citations

• On the triviality of the direct image of coherent sheaves

Cited by

• On the triviality of the direct image of coherent sheaves
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