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Ulrich bundles on cyclic coverings of projective spaces
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abstract
We prove the existence of Ulrich bundles on cyclic coverings of $\mathbb{P}^n$ 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 $\mathbb{P}^{2}$ of degree $d$, provided that the degree $d \cdot k$ of the branch divisor is even. When $d \cdot k$ is odd, we also provide an estimation of the rank of the Ulrich bundle on a generic cyclic covering of $\mathbb{P}^2$.
Forward citations
Cited by 2 Pith papers
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Ulrich bundles on double coverings of projective space
The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.
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On the triviality of direct image of coherent sheaves
For smooth abelian Galois covers, a relatively Ulrich bundle exists exactly when each branch divisor is a sum of d_i-fold tensor products of global sections; so every smooth abelian cover of P^n has an Ulrich bundle.
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