Related papers: Echelon modification of vector bundles
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
We define and explore the notion of linear weightings for vector bundles, extending the recent work by Loizides and Meinrenken. We construct weighted normal bundles and deformation spaces in the category of vector bundles. We explain how a…
By considering the equivalence between the category of locally free sheaves and the category of algebraic vector bundles, we show how elementary transformations of vector bundles can be used to prove a case of the maximal rank hypothesis.…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…
We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a…
We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…
Multigraded linear series generalize the classical morphism to the linear series of a basepoint-free line bundle on a scheme. We investigate the collection of the natural cornering morphisms into elementary bigraded linear series obtained…
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
Hecke modifications of vector bundles have played a significant role in several areas of mathematics. They appear in subjects ranging from number theory to complex geometry. This article intends to be a friendly introduction to the subject.…
A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be…
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
We show that on a generic curve, a bundle obtained by successive extensions is stable. We compute the dimension of the set of such extensions. We use degeneration methods specializing the curve to a chain of elliptic components
For linear flows on vector bundles, it is analyzed when subbundles in the Selgrade decomposition yield chain transitive subsets for the induced flow on the associated Poincar\'e sphere bundle.
In this paper we approach the study of generalized theta linear series on moduli of vector bundles on curves via vector bundle techniques on abelian varieties. We study what are called the Verlinde bundles in order to obtain information…
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to…
We generalize to vector bundles the techniques introduced for line bundles in prior work of the author with Liu, Osserman and Zhang. We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity…