scholarly journals Effective vanishing theorems for ample and globally generated vector bundles

2015 ◽  
Vol 23 (4) ◽  
pp. 797-818 ◽  
Author(s):  
Kefeng Liu ◽  
Xiaokui Yang
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

scholarly journals Positivity and vanishing theorems for ample vector bundles

2012 ◽  
Vol 22 (2) ◽  
pp. 303-331 ◽  
Author(s):  
Kefeng Liu ◽  
Xiaofeng Sun ◽  
Xiaokui Yang
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

Hodge and Vanishing Theorems on Complex Finsler Vector Bundles

2019 ◽  
Author(s):  
Jinling Li ◽  
Chunhui Qiu ◽  
Tongde Zhong
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

scholarly journals Vanishing theorems for ample vector bundles

1997 ◽  
Vol 127 (2) ◽  
pp. 401-416 ◽  
Author(s):  
Laurent Manivel
Keyword(s):  
Vector Bundles ◽  
Vanishing Theorems

Holomorphic Vanishing Theorems on Finsler Holomorphic Vector Bundles and Complex Finsler Manifolds

2018 ◽  
Vol 62 (3) ◽  
pp. 623-641
Author(s):  
Bin Shen
Keyword(s):  
Vector Fields ◽  
Vector Bundles ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Vanishing Theorems ◽  
Complex Manifolds ◽  
Finsler Manifolds ◽  
Holomorphic Vector Fields ◽  
Holomorphic Vector Bundles ◽  
Holomorphic Sections

AbstractIn this paper, we investigate the holomorphic sections of holomorphic Finsler bundles over both compact and non-compact complete complex manifolds. We also inquire into the holomorphic vector fields on compact and non-compact complete complex Finsler manifolds. We get vanishing theorems in each case according to different certain curvature conditions. This work can be considered as generalizations of the classical results on Kähler manifolds and hermitian bundles.

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