Uniform Vector Bundles on Fano Manifolds and an Algebraic Proof of Hwang-Mok Characterization of Grassmannians

2002 ◽  
pp. 329-340 ◽  
Author(s):  
Jarosław A. Wiśniewski
Keyword(s):  
Vector Bundles ◽  
Algebraic Proof ◽  
Fano Manifolds

scholarly journals EQUATIONS OF THE MODULI OF HIGGS PAIRS AND INFINITE GRASSMANNIAN

2009 ◽  
Vol 20 (08) ◽  
pp. 1029-1055 ◽  
Author(s):  
D. HERNÁNDEZ-SERRANO ◽  
J. M. MUÑOZ PORRAS ◽  
F. J. PLAZA MARTÍN
Keyword(s):  
Fixed Point ◽  
Moduli Space ◽  
Vector Bundles ◽  
Higgs Field ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Spectral Cover ◽  
Relative Version ◽  
Moduli Of Vector Bundles

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato Grassmannians and show that this map is injective. This, together with the characterization of the points of the image of the Krichever map, allows us to prove that this moduli space is a closed subscheme of the product of the moduli of vector bundles (with formal extra data) and a formal anologue of the Hitchin base. This characterization also provides us with a method for explicitly computing KP-type equations that describe the moduli space of Higgs pairs. Finally, for the case where the spectral cover is totally ramified at a fixed point of the curve, these equations are given in terms of the characteristic coefficients of the Higgs field.

scholarly journals Uniform vector bundles on Fano manifolds and applications

2012 ◽  
Vol 2012 (664) ◽  
Author(s):  
Roberto Muñoz ◽  
Gianluca Occhetta ◽  
Solá Conde Luis E.
Keyword(s):  
Vector Bundles ◽  
Fano Manifolds

scholarly journals Jacobi geometry and Hamiltonian mechanics: The unit-free approach

2020 ◽  
Vol 17 (12) ◽  
pp. 2030005
Author(s):  
Carlos Zapata-Carratalá
Keyword(s):  
Vector Bundles ◽  
Mathematical Framework ◽  
Poisson Geometry ◽  
Hamiltonian Mechanics ◽  
Systematic Treatment ◽  
Straightforward Manner ◽  
Jacobi Manifolds ◽  
Categorical Structure ◽  
Physical Quantities

We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalize the ordinary categories of smooth manifolds and vector bundles to account for a lack of choice of a preferred unit, which in standard differential geometry is always given by the global constant function [Formula: see text]. This is what we call the “unit-free” approach. After giving a characterization of local Lie brackets via their symbol maps, we apply our novel categorical language to review Jacobi manifolds and related notions such as Lichnerowicz brackets and Jacobi algebroids. The main advantage of our approach is that Jacobi geometry is recovered as the direct unit-free generalization of Poisson geometry, with all the familiar notions translating in a straightforward manner. We then apply this formalism to the question of whether there is a unit-free generalization of Hamiltonian mechanics. We identify the basic categorical structure of ordinary Hamiltonian mechanics to argue that it is indeed possible to find a unit-free analogue. This paper serves as a prelude to the investigation of dimensioned structures, an attempt at a general mathematical framework for the formal treatment of physical quantities and dimensional analysis.

On the splitting type of holomorphic vector bundles induced from regular systems of differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Grigori Giorgadze ◽  
Gega Gulagashvili
Keyword(s):  
Vector Bundles ◽  
Riemann Sphere ◽  
Complete Characterization ◽  
Fuchsian System ◽  
Hölder Continuous ◽  
Holomorphic Vector Bundles ◽  
Splitting Type ◽  
Second Order Systems ◽  
The Relationship

Abstract We calculate the splitting type of holomorphic vector bundles on the Riemann sphere induced by a Fuchsian system of differential equations. Using this technique, we indicate the relationship between Hölder continuous matrix functions and a moduli space of vector bundles on the Riemann sphere. For second order systems with three singular points we give a complete characterization of the corresponding vector bundles by the invariants of Fuchsian system.

Fano manifolds and vector bundles

1992 ◽  
Vol 294 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Thomas Peternell ◽  
Michal Szurek ◽  
Jaroslaw A. Wisniewski
Keyword(s):  
Vector Bundles ◽  
Fano Manifolds

scholarly journals On Monge–Ampère Volumes of Direct Images

2021 ◽  
Author(s):  
Siarhei Finski
Keyword(s):  
Vector Bundles ◽  
Ample Line Bundle ◽  
Symmetric Powers ◽  
Projectively Flat ◽  
Leading Term ◽  
Tensor Powers ◽  
Monge Ampere ◽  
Hermitian Structures

Abstract This paper is devoted to the study of the asymptotics of Monge–Ampère volumes of direct images associated with high tensor powers of an ample line bundle. We study the leading term of this asymptotics and provide a classification of bundles saturating the topological bound of Demailly. In the special case of high symmetric powers of ample vector bundles, this provides a characterization of those admitting projectively flat Hermitian structures.

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