During the last years there has been growing interest in vector bundles with additional structures, e.g. parabolic and level structures. This paper results from an attempt to construct quasi-projective moduli spaces for framed bundles, i.e. bundles together with an isomorphism to a fixed bundle on a divisor as introduced in [Do], [L1] and [Lü]. More generally one can ask for bundles with a homo...

For a rank two vector bundle E on the projective plane IP the divisor DE of its jumping lines is a certain generalization of the Chow divisor of a projective scheme We give a generalization of this divisor for coherent sheaves on surfaces Using this duality we construct the moduli space of coherent sheaves on a surface that does not use Mumford s geometric invariant theory Furthermore we obtain...

This article is a survey of recent work [15, 6, 7, 13] developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential geometry: given a smooth manifold M endowed with a flat conformal/projective structure, we establish a canonical isomorphism between the space of symmetric contravar...

We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality statements about SecX and also to obtain information about linear systems on the blow up of projective space along a variety X. We use these results to geometrica...

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants cross products. These proved to hold in three-dimensional vector space field. They closely related Arguesian identity lattice theory Cayley-Grassmann invariant theory.

In a recent paper, Dave Benson and Peter Symonds defined new invariant ?G(M) for finite dimensional module M of group G which attempts to quantify how close is being projective. this we determine permutation modules the symmetric corresponding two-part partitions using tools from representation theory combinatorics.

It was shown by Samelson [9] and Wang [10] that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently by Charbonnel and Khalgui [2] who have also given a complete algebraic description of these structures. In this article we present an alternative a...

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used...

A general framework for integration over certain innnite dimensional spaces is rst developed using projective limits of a projective family of compact Hausdorr spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, innnite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used eith...