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Marian Aprodu Laura Costa Rosa Maria Miró-Roig 《Journal of Pure and Applied Algebra》2018,222(1):131-138
In this short note, we study the existence problem for Ulrich bundles on polarized ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient α of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles. 相似文献
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We prove that the vector bundle associated to a Galois covering of projective manifolds is ample (resp. nef) under very mild
conditions. This results is applied to the study of ramified endomorphisms of Fano manifolds with b
2 = 1. It is conjectured that is the only Fano manifold admitting an endomorphism of degree d ≥ 2, and we verify this conjecture in several cases. An important ingredient is a generalization of a theorem of Andreatta–Wisniewski,
characterizing projective space via the existence of an ample subsheaf in the tangent bundle.
Marian Aprodu was supported in part by a Humboldt Research Fellowship and a Humboldt Return Fellowship. He expresses his special
thanks to the Mathematical Institute of Bayreuth University for hospitality during the first stage of this work. Stefan Kebekus
and Thomas Peternell were supported by the DFG-Schwerpunkt “Globale Methoden in der komplexen Geometrie” and the DFG-Forschergruppe
“Classification of Algebraic Surfaces and Compact Complex Manifolds”. A part of this paper was worked out while Stefan Kebekus
visited the Korea Institute for Advanced Study. He would like to thank Jun-Muk Hwang for the invitation. 相似文献
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Marian Aprodu Vasile Brînzănescu Marius Marchitan 《Central European Journal of Mathematics》2012,10(4):1321-1330
We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on the rank-two case. 相似文献