scholarly journals Strictly nef vector bundles and characterizations of ℙ n

2021 ◽  
Vol 8 (1) ◽  
pp. 138-149
Author(s):  
Jie Liu ◽  
Wenhao Ou ◽  
Xiaokui Yang
Keyword(s):  
Vector Bundles ◽  
Projective Manifolds ◽  
Nef Vector Bundles

Abstract In this note, we give a brief exposition on the differences and similarities between strictly nef and ample vector bundles, with particular focus on the circle of problems surrounding the geometry of projective manifolds with strictly nef 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.

Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles

2008 ◽  
Vol 144 (1) ◽  
pp. 109-118 ◽  
Author(s):  
ANTONIO LANTERI ◽  
HIDETOSHI MAEDA
Keyword(s):  
Vector Bundles ◽  
Projective Variety ◽  
Ample Line Bundle ◽  
Global Section ◽  
Sectional Genus ◽  
Ample Vector Bundle ◽  
Complex Projective Variety ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Zero Locus

AbstractLet ϵ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section of ϵ whose zero locus Z is a smooth subvariety of dimension n-r ≥ 2 of X. Let H be an ample line bundle on X such that the restriction HZ of H to Z is very ample. Triplets (X, ϵ, H) with g(Z, HZ) = 3 are classified, where g(Z, HZ) is the sectional genus of (Z, HZ).

scholarly journals Mirror symmetry for concavex vector bundles on projective spaces

2003 ◽  
Vol 2003 (3) ◽  
pp. 159-197 ◽  
Author(s):  
Artur Elezi
Keyword(s):  
Mirror Symmetry ◽  
Vector Bundles ◽  
Projective Spaces ◽  
Witten Theory ◽  
Generic Section ◽  
Projective Manifolds ◽  
Local Mirror Symmetry ◽  
Zero Locus

LetX⊂Ybe smooth, projective manifolds. Assume thatι:X→ℙsis the zero locus of a generic section ofV+=⊕i∈I𝒪(ki), where all theki's are positive. Assume furthermore that𝒩X/Y=ι∗(V−), whereV−=⊕j∈J𝒪(−lj)and all thelj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants ofXinherited fromYcan be calculated via a modified Gromov-Witten theory onℙs. This leads to local mirror symmetry on theA-side.

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 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
Sign in / Sign up

Export Citation Format

Share Document