Characteristic classes of stable bundles of rank $2$ over an algebraic curve

Characteristic Classes of Stable Bundles of Rank 2 over an Algebraic Curve

Let X be a complete nonsingular algebraic curve over C and L a line bundle of degree 1 over X. It is well known that the isomorphism classes of stable bundles of rank 2 and determinant L over X form a nonsingular projective variety S(X). The Betti numbers of S(X) are also known. In this paper we define certain distinguished cohomology classes of S(X) and prove that these classes generate the ra...

Algebraic Theory of Characteristic Classes of Bundles with Connection

Restriction of stable rank two vector bundles in arbitrary characteristic

Let X be a smooth variety de ned over an algebraically closed eld of arbitrary characteristic and OX H be a very ample line bundle on X We show that for a semistable X bundle E of rank two there exists an integer m depending only on E H X and H X such that the restric tion of E to a general divisor in jmH j is again semistable As corollaries we obtain boundedness results and weak versions of Bo...

Characteristic classes of complexified bundles

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from real vector bundles are computed. We use characteristic classes with the axioms of Milnor and Stasheff [6]. Introduction Definition (Real generator bundles). We consider a real vector bundle F → B and a complex vector bundle E → B over the same base space B. If...

Characteristic Classes of A{bundles

We consider locally trivial bundles over smooth manifolds, whose fibers are finitely generated projective modules over a convenient algebra A. For such a bundle E → X and a bounded reduced cyclic cocycle c on A we construct a sequence chc (E) of de–Rham cohomology classes on X, which are an analog of the classical Chern character. We show that these classes depend only on the cohomology class o...