Related papers: ADE Bundles over Surfaces
Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible)…
Based on the Brieskorn-Slodowy-Grothendieck diagram, we write the holomorphic structures (or filtrations) of the ADE Lie algebra bundles over the corresponding type ADE flag varieties, over the cotangent bundles of these flag varieties, and…
To each del Pezzo surface (resp. ruled surface, ruled surface with a section), we describe a natural Lie algebra bundle of type E_n (resp. D_n, A_n) over it. Using lines and rulings on any such surface, we describe various representation…
It is well-known that del Pezzo surfaces of degree $9-n$ one-to-one correspond to flat $E_n$ bundles over an elliptic curve. In this paper, we construct $ADE$ bundles over a broader class of rational surfaces which we call $ADE$ surfaces,…
We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that…
We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…
This note will become part of a new paper with more authors.
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these results to double Lie algebroids and LA-groupoids.
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
We investigate topological properties of torsors in algebraic geometry over adelic rings.
We study flat vector bundles over complex parallelizable manifolds.
A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…
This work provides a curve-based approach to Ulrich bundles on surfaces, establishing a correspondence that characterizes their existence, with a focus on applications to surfaces in $\mathbb{P}^3$.
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of…
We construct symplectic surface bundles over surfaces with positive signatures for all but 18 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.