Let M be a K3 surface or a 2-dimensional compact torus, B a stable bundle on M , and X the coarse moduli of stable deformations of B. The Fourier-Mukai transform is a functor FM : Db(M)−→Db(X), where Db(M), Db(X) denotes the derived category of coherent sheaves on M , X . Consider a stable bundle B1 on M , and let FM(B1) be the corresponding complex of coherent sheaves onX . AssumeX is compact....

We study quotients of multi-graded bundles, including double vector bundles. Among other things, we show that any such quotient fits into a tower affine Applications the theory include construction normal bundles for weighted submanifolds, as well pairs submanifolds with clean intersection.

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to diierent ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

We develop a holomorphic equivalence between on one hand the space of pairs (stable bundle, flat connection bundle) and sheaf connections (the splittings one-jet sequence) for determinant (Quillen) line bundle over moduli vector bundles compact connected Riemann surface. This is shown to be holomorphically symplectic. The equivalences, both symplectic, seem quite general, in that they extend ot...

Abstract Let π −→ X be a principal elliptic fibration over a Kähler base X . We assume that the Kähler form on X is lifted to an exact form on M (such fibrations are called positive). Examples of these are regular Vaisman manifolds (in particular, the regular Hopf manifolds) and Calabi-Eckmann manifolds. Assume that dimM > 2. Using the KobayashiHitchin correspondence, we prove that all stable b...

We show that the R/Z part of the analytically defined η invariant of Atiyah-PatodiSinger for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, we discuss the relation with the Atiyah-PatodiSinger R/Z index theorem for unitary flat vector bundles, an...