Vector bundles on curves and p-adic Hodge theory

2014 ◽  
pp. 17-104 ◽  
Author(s):  
Laurent Fargues ◽  
Jean-Marc Fontaine
Keyword(s):  
Vector Bundles ◽  
Hodge Theory

scholarly journals Positivity of vector bundles and Hodge theory

2021 ◽  
pp. 2140008
Author(s):  
Mark Green ◽  
Phillip Griffiths
Keyword(s):  
Differential Geometry ◽  
Vector Bundles ◽  
Special Property ◽  
Hodge Theory ◽  
Algebraic Varieties ◽  
Hodge Structures ◽  
Curvature Invariants ◽  
Norm Property ◽  
Expository Paper

Differential geometry, especially the use of curvature, plays a central role in modern Hodge theory. The vector bundles that occur in the theory (Hodge bundles) have metrics given by the polarizations of the Hodge structures, and the sign and singularity properties of the resulting curvatures have far reaching implications in the geometry of families of algebraic varieties. A special property of the curvatures is that they are [Formula: see text] order invariants expressed in terms of the norms of algebro-geometric bundle mappings. This partly expository paper will explain some of the positivity and singularity properties of the curvature invariants that arise in the Hodge theory with special emphasis on the norm property.

scholarly journals Asymptotic Hodge theory of vector bundles

2015 ◽  
Vol 23 (3) ◽  
pp. 559-609
Author(s):  
Benoit Charbonneau ◽  
Mark Stern
Keyword(s):  
Vector Bundles ◽  
Hodge Theory

scholarly journals Toric vector bundles: GAGA and Hodge theory

2020 ◽  
Author(s):  
Jonas Stelzig
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Hodge Theory ◽  
Algebraic Construction ◽  
Smooth Base

Abstract We prove a GAGA-style result for toric vector bundles with smooth base and give an algebraic construction of the Frölicher approximating vector bundle that has recently been introduced by Dan Popovici using analytic techniques. Both results make use of the Rees-bundle construction.

scholarly journals Nonabelian Hodge theory for klt spaces and descent theorems for vector bundles

2019 ◽  
Vol 155 (2) ◽  
pp. 289-323 ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Thomas Peternell ◽  
Behrouz Taji
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Projective Variety ◽  
Hodge Theory ◽  
Resolution Of Singularities ◽  
Independent Interest ◽  
Restriction Theorem ◽  
Projective Varieties ◽  
To Come ◽  
Smooth Locus

We generalise Simpson’s nonabelian Hodge correspondence to the context of projective varieties with Kawamata log terminal (klt) singularities. The proof relies on a descent theorem for numerically flat vector bundles along birational morphisms. In its simplest form, this theorem asserts that given any klt variety$X$and any resolution of singularities, any vector bundle on the resolution that appears to come from$X$numerically, does indeed come from $X$. Furthermore, and of independent interest, a new restriction theorem for semistable Higgs sheaves defined on the smooth locus of a normal, projective variety is established.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Teichmüller dynamics and unique ergodicity via currents and Hodge theory

2020 ◽  
Vol 2020 (768) ◽  
pp. 39-54
Author(s):  
Curtis T. McMullen
Keyword(s):  
Hodge Theory ◽  
Unique Ergodicity ◽  
Polygonal Billiards ◽  
Teichmuller Dynamics

AbstractWe present a cohomological proof that recurrence of suitable Teichmüller geodesics implies unique ergodicity of their terminal foliations. This approach also yields concrete estimates for periodic foliations and new results for polygonal billiards.

scholarly journals Fano 3-folds from homogeneous vector bundles over Grassmannians

2021 ◽  
Author(s):  
Lorenzo De Biase ◽  
Enrico Fatighenti ◽  
Fabio Tanturri
Keyword(s):  
Vector Bundles ◽  
Homogeneous Vector

AbstractWe rework the Mori–Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.

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