The present paper is devoted to the study of vector bundles with an additional structure from a unified point of view. We have picked the name " decorated vector bundles " suggested in . Before we outline our paper, let us give some background. The first problem to treat is the problem of classifying vector bundles over an algebraic curve X, assumed… (More)
In this paper we shall construct master spaces for certain coupled vector bundle problems over a fixed projective variety X. These master spaces, which are moduli spaces for oriented torsion free coherent sheaves coupled with morphisms into a fixed reference sheaf E 0 , have the structure of polarized projective varieties endowed with a natural C *-action.… (More)
Introduction In the paper , Hitchin studied pairs (E, ϕ), where E is a vector bundle of rank two with a fixed determinant on a curve C and ϕ : E −→ E ⊗ K C is a trace free homomorphism, and constructed a moduli space for them. This moduli space carries the structure of a non-complete, quasi-projective algebraic variety. Later, Nitsure  gave an… (More)
In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.
We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers.
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Graßmannian. It has all the properties asked for by Teixidor.
In this paper, we will be concerned with the explicit classification of closed, oriented, simply-connected spin manifolds in dimension eight with vanishing cohomology in the odd dimensions. The study of such manifolds was begun by Stefan Müller. In order to understand the structure of these manifolds, we will analyze their minimal handle presentations and… (More)
An important classification problem in Algebraic Geometry deals with pairs (E, ϕ), consisting of a torsion free sheaf E and a non-trivial homomorphism ϕ: (E ⊗a) ⊕b −→ det(E) ⊗c ⊗ L on a polarized complex projective manifold (X, O X (1)), the input data a, b, c, L as well as the Hilbert polynomial of E being fixed. The solution to the classification problem… (More)
Let G ¢ X X be an action of the reductive group G on the projective scheme X. For every linearization σ of this action in an ample line bundle, there is an open set X ss σ of σ-semistable points. We provide an elementary and geometric proof for the fact that there exist only finitely many open sets of the form X ss σ. In characteristic zero, this… (More)
We prove the equivalence of the notions of Hilbert (semi)stability and Mum-ford (semi)stability for vector bundles on smooth curves for arbitrary rank.