Related papers: Vector bundles, linear representations, and spectr…

Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and important, since they provide a simple reconstruction scheme and are…

A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…

The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…

The study of the volume of big line bundles on a complex projective manifold M has been one of the main veins in the recent interest in the asymptotic properties of linear series. In this article, we consider an equivariant version of this…

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…

We give a canonical description of the formal moduli space of a vector bundle on a variety; as an application, we prove the closedness of certain differential forms on moduli corresponding to the trace form on the endomorphism algebra of…

We study stable vector bundles over the modular curve X(p) corresponding to the principal congruence subgroup of the modular group of prime level p which are invariant with respect to its automorphism group.

We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…

We introduce an algebra of Schouten-commuting holomorphic polyvector fields on the moduli space of stable G-bundles over a curve by using invariant forms on the Lie algebra. The generators begin in degree three -- we prove a vanishing…

An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…

This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…

In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…

We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…

A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…

We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…