Related papers: Moduli of vector-bundles on surfaces
This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.
We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.
This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.
In this article, we study the smoothness of the moduli space of finite quiver vector bundles over the smooth complex projective curves.
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…
This note will become part of a new paper with more authors.
We discuss some relations of moduli of sheaves on rational surfaces by using universal extensions. These are a generalization of Maruyama's method to construct Uhlenbeck compactification of moduli of vector bundles.
We construct new stable vector bundles on Hilbert schemes of points on algebraic surfaces, which are parametrised by connected components of their moduli spaces. This work generalises aspects of our previous work on tautological bundles and…
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
This is a (short) survey lecture on the "theta map" from the moduli space of SL_r bundles on a curve C to the projective space of r-th order theta functions on JC . Some recent results and a few open problems about that map are discussed.
This is a survey paper discussing the moduli problem for varieties of general type.
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.
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a M\"obius type action of an automorphism group on a space of…
In this paper, we survey recent developments in the Brill-Noether Theory of higher rank vector bundles on complex projective surfaces. We focus on weak Brill-Noether Theorems on rational and K-trivial surfaces and their applications.
This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…
The main purpose in this paper is to study exceptional vector bundles on Enriques surfaces.
We study flat vector bundles over complex parallelizable manifolds.
We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…