DEFORMING TORSION-FREE SHEAVES ON AN ALGEBRAIC SURFACE

Abstract

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.