scholarly journals Generically nef vector bundles on ruled surfaces

2018 ◽  
Vol 198 (2) ◽  
pp. 443-463
Author(s):  
Beorchia Valentina ◽  
Zucconi Francesco
Keyword(s):  
Vector Bundles ◽  
Ruled Surfaces ◽  
Nef Vector Bundles

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

Nef vector bundles on a quadric surface with the first Chern class (2, 1)

2020 ◽  
Vol 20 (1) ◽  
pp. 109-116
Author(s):  
Masahiro Ohno
Keyword(s):  
Chern Class ◽  
Characteristic Zero ◽  
Vector Bundles ◽  
Closed Field ◽  
Quadric Surface ◽  
Algebraically Closed Field ◽  
First Chern Class ◽  
Smooth Quadric Surface ◽  
Nef Vector Bundles

AbstractWe classify nef vector bundles on a smooth quadric surface with the first Chern class (2, 1) over an algebraically closed field of characteristic zero; we see in particular that such nef bundles are globally generated.

scholarly journals Rank-two vector bundles on non-minimal ruled surfaces

2017 ◽  
Vol 370 (6) ◽  
pp. 3913-3929
Author(s):  
Marian Aprodu ◽  
Laura Costa ◽  
Rosa Maria Miró-Roig
Keyword(s):  
Vector Bundles ◽  
Ruled Surfaces
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