We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a perfect complex on a ringed space. 1991 Mathematics Subject Classi cation: Primary: 16E40; Secondary: 18E30, 14F05.

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kähler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to ...

In [6], the geometric dimension of all stable vector bundles over real projective space P was determined if n is even and sufficiently large with respect to the order 2 of the bundle in K̃O(P). Here we perform a similar determination when n is odd and e > 6. The work is more delicate since P does not admit a v1-map when n is odd. There are a few extreme cases which we are unable to settle precis...

Here we investigate meaningful families of vector bundles on a very general polarized K3 surface (X, H) and the corresponding Hyper–Kähler variety given by Hilbert scheme points $$X^{[k]}:= {\textrm{Hilb}}^k(X)$$ , for any integer $$k \geqslant 2$$ . In particular, prove results concerning bigness stability such bundles. First, give conditions integers n that twist tangent bundle X line nH is b...

Preface Topological K–theory, the first generalized cohomology theory to be studied thoroughly , was introduced around 1960 by Atiyah and Hirzebruch, based on the Periodic-ity Theorem of Bott proved just a few years earlier. In some respects K–theory is more elementary than classical homology and cohomology, and it is also more powerful for certain purposes. Some of the best-known applications ...

Given a holomorphic vector bundle F over a compact Riemann surface X, and a subspace Sx ⊂ Fx in the fiber over a point x, the Hecke transformation produces a new vector bundle E on X [10, 16]. The vector bundle E is the kernel of the natural quotient map F −→ Fx/Sx. Hecke transformation is a very useful tool to study the moduli space. For instance, they are used in computation of cohomologies o...