Related papers: Root stacks, principal bundles and connections

For a normal algebraic variety we generalise the relation between reflexive rank one sheaves and Weil divisors to reflexive sheaves of arbitrary rank and so-called Weil decorations. As an application, we define and study a natural…

We introduce the notion of \textbf{Q}-principal bundle, which is the appropriate version of principal fibre bundles in the setting of R. Barre's \textbf{Q}-manifolds. As an application, we prove that every transitive Lie algebroid arises…

This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it…

This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…

We classify the reflexive modules of rank one over rational and minimally elliptic singularities. Equivalently, we classify full line bundles on the resolutions of rational and minimally elliptic singularities. As an application, we…

In this paper we introduce the concept of Abelian integrals in differential equations for an arbitrary vector bundle on $\P1$ with a meromorphic connection. In this general context we give an upper bound for the numbers we are looking for.

The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher…

For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, we prove the existence of a canonical…

We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.

For complex connected, reductive, affine, algebraic groups $G$, we give a Lie-theoretic characterization of the semistability of principal $G$-co-Higgs bundles on the complex projective line $\mathbb{P}^1$ in terms of the simple roots of a…

In this note we prove that the moduli stack of vector bundles on a curve, with a fixed determinant is $\mathbb{A}^1$-connected. We obtain this result by classifying vector bundles on a curve upto $\mathbb{A}^1$-concordance. Consequently we…

We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \sigma and \tau induced by isogenies of relatively prime orders. We give a structure theorem for such objects, that…

In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…

Let M be a paracompact smooth manifold of dimension n; A a Weil algebra and M^A the Weil bundle associated. We define and describe the notion of \widetilded-Poisson cohomology and of \widetilded^A -Poisson cohomology on M^A.

We generalize principal bundles and quotient stacks to the two-categorical context of bisites. We introduce a notion of principal 2-bundle that makes sense for a 2-category with finite flexible limits, endowed with a bitopology. We then use…

Let $C$ be an irreducible smooth projective curve of genus $g\geq 2$ over an algebraically closed field. We prove that the moduli stack of semi-stable vector bundles on $C$ of fixed rank and determinant is $\mathbb{A}^1$--connected. We also…

We establish the existence of rank two Ulrich vector bundles on surfaces that are either of maximal Albanese dimension or with irregularity 1, under many embeddings. In particular we get the first known examples of Ulrich vector bundles on…

Let $\mathbb{X}=[X_1\rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mathcal{H} \subset T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution…

Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…

Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.