Let [Formula: see text] be a polarized nodal reducible curve. In this paper, we consider coherent systems of type on with text]. We prove that the moduli spaces text]-stable stabilize for large and generalize several results known irreducible case when choose good polarization. Then, study in detail components containing arising from locally free sheaves.

We construct and describe moduli spaces of Azumaya algebras on a smooth projective surface. These spaces are the algebro-geometric version of the spaces of principal PGL n -bundles and they also have strong connections to arithmetic. A geometric approach to the problem leads one to study moduli spaces of twisted sheaves. We show that these spaces are very similar to the moduli spaces of semi-st...

We describe a method for characterizing certain connected components of the moduli space M(a; b) of torsion-free sheaves on a elliptic surface X with a section which are stable with respect to a polarization of type aH + bb, H being the section and the elliptic bre (b 0) and whose relative degree is zero. We construct all sheaves in these components as Fourier-Mukai transforms of the pure dimen...

Last time, we began analyzing geometrically ruled surfaces by studying projectivizations of rank 2 locally free sheaves. We proved: Proposition. Every geometrically ruled surface over C is C-isomorphic to PC(E) for some rank 2 locally free sheaf (vector bundle) over C. The bundles PC(E) and PC(E ′) are isomorphic (over C) iff there is an invertible sheaf (line bundle) L on C such that E ′ ∼= E ...

We show that Boehmians defined over open sets of R constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over topological spaces. MSC: Primary 44A40, 46F99; Secondary 44A35, 18F20

A ‘Chen space’ is a set X equipped with a collection of ‘plots’ — maps from convex sets to X — satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold, the category of all Chen spaces is much better behaved than the category of smooth manifolds. For example, any subspace or quotient space of a Chen space is a Chen space, and the space of smooth ma...

Let X be a projective manifold over C. Fix two ample line bundles H0 and H1 on X. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lieing in the cone spanned by H0 and H1. We attempt a new definition of walls which naturally describes the behaviour of Gieseker semistability. By means of an example, we establish the possibili...

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. resolve a serious deficit in existing theory by constructing good notion of presheaves, with suitable sheafification functor. Using sheafification, we develop general modules ring, give explicit constructions infinite products and introduce an analogue skyscraper sheaves. These results underlie re...

We study the cohomology of invertible sheaves C on surfaces X, blowings-up of P2 at points pl,...,p, in general position (generic rational surfaces). The main theme is when such sheaves have the natural cohomology, i.e. at most one cohomology group is non zero. Our approach is geometrical. On one hand we are lead to deform the configuration of points to a special position, notably surfaces with...