On Deformation of Sheaves

Let be an algebraic variety over an algebraically closed field , a sheaf on , and commutative Artinian -algebras, , where is a one-dimensional ideal, a deformation of with base , and the obstruction to the extension of the deformation to . The author constructs natural trace maps and proves that if is nonsingular then . As a consequence, a universal deformation of a simple sheaf on with nonsingular exists if the map is injective or, in the case , and , . Bibliography: 3 titles.