tautological line bundle
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Author(s):  
Maria Lucia Fania ◽  
Margherita Lelli-Chiesa ◽  
Joan Pons-Llopis

Abstract In this paper we construct Ulrich bundles of low rank on three-dimensional scrolls (with respect to the tautological line bundle). We pay special attention to the four types of three-fold scrolls in ${\mathbb{P}}^5$, which were classified in [31].


Author(s):  
Xiaokui Yang

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle ${\mathcal{O}}_{T_{M}^{\ast }}(1)$ is not pseudo-effective and ${\mathcal{O}}_{T_{N}^{\ast }}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$ . In particular, we prove that any holomorphic map from a compact complex manifold $M$ with RC-positive tangent bundle to a compact complex manifold $N$ with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.


2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Shintarô Kuroki ◽  
Zhi Lü

AbstractThe present paper investigates the projective bundles over small covers. We first give a necessary and sufficient condition for the projectivization of a real vector bundle over a small cover to be a small cover. Then associated with moment-angle manifolds, we further study the structure of such a projectivization as a small cover by introducing a new characteristic function on simple convex polytopes. As an application, we characterize the real projective bundles over 2-dimensional small covers by interpreting the fiber sum operation to some combinatorial operation. We next determine when the projectivization of Whitney sum of the tautological line bundle and the tangent bundle over real projective space is diffeomorphic to the product of two real projective spaces. This answers an open question regarding the topology of the fiber of the Monster-Semple tower.


2011 ◽  
Vol 22 (11) ◽  
pp. 1647-1660 ◽  
Author(s):  
INDRANIL BISWAS ◽  
FATIMA LAYTIMI

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle E* is defined to be k-ample if the tautological line bundle [Formula: see text] is k-ample. We establish some properties of parabolic k-ample bundles.


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