Related papers: A Cubical Set Approach to 2-Bundles with Connectio…
For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line…
We classify principal bundles over anti-affine schemes with affine and commutative structural group. We show that this yields the classification of quasi-abelian varieties over a field k (i.e., group k-schemes with no non constant global…
We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of…
We show birationality of the morphism associated to line bundles $L$ of type $(1,...,1,2,...,2,4,...,4)$ on a generic $g-$dimensional abelian variety into its complete linear system such that $h^0(L)=2^g$. When $g=3$, we describe the image…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
Surface holonomy and the Wess-Zumino phase play a central role in string theory and Chern-Simons models, yet a completely analytic formulation of their nonabelian counterparts has remained elusive. In this work, we show that Yekutieli's…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the…
We study the set of isomorphism classes of principal polarizations on abelian varieties of GL2-type. As applications of our results, we construct examples of curves C, C'/\Q of genus two which are nonisomorphic over \bar \Q and share…
In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real…
We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an…
To a family of smooth projective cubic surfaces one can canonically associate a family of abelian fivefolds. In characteristic zero, we calculate the Hodge groups of the abelian varieties which arise in this way. In arbitrary characteristic…
The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences…
We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric…
Our main aim is to associate a holonomy Lie groupoid to the connective structure of an abelian gerbe. The construction has analogies with a procedure for the holonomy Lie groupoid of a foliation, in using a locally Lie groupoid and a…
Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this is known to be related to the…
We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our…
In a previous work, the authors gave a definition of `front bundles'. Using this, we give a realization theorem for wave fronts in space forms, like as in the fundamental theorem of surface theory. As an application, we investigate the…
We study gauge theories based on nonabelian 2-forms. Certain connections on loop space give rise to generalized covariant derivatives that include a nonabelian 2-form. This can be used to find rather straightforward expressions for the…
We exhibit a closed aspherical 5-manifold of nonpositive curvature that fibers over a circle whose fundamental group is hyperbolic relative to abelian subgroups such that the fiber is a closed aspherical 4-manifold whose fundamental group…