Moduli Space Of Stable Bundles Research Articles

DEFORMING TORSION-FREE SHEAVES ON AN ALGEBRAIC SURFACE

This paper investigates the question of removability of singularities of torsion-free sheaves on algebraic surfaces in the universal deformation and the existence in it of a nonempty open set of locally free sheaves, and describes the tangent cone to the set of sheaves having degree of singularities larger than a given one. These results are used to prove that quasitrivial sheaves on an algebraic surface with (r + 1) \max(1, p_g(X))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img3.gif/> have a universal deformation whose general sheaf is locally free and stable relative to any ample divisor on , and thereby to find a nonempty component of the moduli space of stable bundles on with and \max(1, p_g(X) \cdot (r + 1))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img5.gif/> on any algebraic surface. Bibliography: 11 titles.

Flat connections and geometric quantization

Using the space of holomorphic symmetric tensors on the moduli space of stable bundles over a Riemann surface we construct a projectively flat connection on a vector bundle over Teichmüller space. The fibre of the vector bundle consists of the global sections of a power of the determinant bundle on the moduli space. Both Dolbeault and Čech techniques are used.

On the relations between characteristic classes of stable bundles of rank 2 over an algebraic curve

We describe a complete set of generators and relations for a certain quotient of the rational cohomology ring of the moduli space of stable bundles of rank 2 and fixed determinant of odd degree over a nonsingular complex algebraic curve. The formulae for the relations apply in any genus and are relatively simple.

A degeneration of the moduli space of stable bundles

A degeneration of the moduli space of stable bundles

Rationality of moduli spaces of stable bundles

Let X be a complete non-singular algebraic curve of genus 9 > 2 over an algebraically closed field k, n a positive integer, d an integer and L a line bundle of degree d over X. It is well known that the isomorphism classes of stable bundles of rank n and determinant L over X form an irreducible non-singular quasiprojective variety S,,L(X) of dimension (n 2 1 ) (9-1) , which is projective if (n,d)= 1 (see [8, 10-13]). It is also easy to see that S,,L(X) is unirational. Our object in this paper is to prove

Rationality of moduli spaces of stable bundles

Rationality of moduli spaces of stable bundles