To understand in detail duality between heterotic string and F theory compactifications, it is important to understand the construction of holomorphic G bundles over elliptic Calabi-Yau manifolds, for various groups G. In this paper, we develop techniques to describe these bundles, and make several detailed comparisons between the heterotic string and F theory.

The notion of quantum group equivariant homogeneous vector bundles on quantum homogeneous spaces is introduced. The category of such quantum vector bundles is shown to be exact, and its Grothendieck group is determined. It is also shown that the algebras of functions on quantum homogeneous spaces are noetherian.

We give a new proof of the vanishing of H1(X, V ) for negative vector bundles V on normal projective varieties X satisfying rank V < dim X. Our proof is geometric, it uses a topological characterization of the affine bundles associated with non-trivial cocycles α ∈ H1(X, V ) of negative vector bundles. Following the same circle of ideas, we use the analytic characteristics of affine bundles to ...

Graph bundles generalize the notion of covering graphs and graph products. In [8], authors constructed an algorithm that ÿnds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base. In [21], the unique square property is deÿned and it is shown that any equivalence relation possessing the unique square property determi...

This paper examines the economic logic underlying bundles and tie-in sales and uses the lessons learned from that examination to analyze seven specific instances of bundling that have been the subject of antitrust scrutiny or other policy initiatives. It is particularly interested in products that are non-rivalrous in consumption, making all-you-can-eat pricing a viable candidate for efficiency...

Parabolic geometries may be considered as curved analogues of the homogeneous spaces G/P where G is a semisimple Lie group and P ⊂ G a parabolic subgroup. Conformal geometries and CR geometries are examples of such structures. We present a uniform description of a calculus, called tractor calculus, based on natural bundles with canonical linear connections for all parabolic geometries. It is sh...

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that genera...

Let A and B be very ample line bundles on a projective toric variety. Then, it is proved that the multiplication map Γ(A)⊗ Γ(B) → Γ(A⊗B) of global sections of the two bundles is surjective. As a consequence, it is showed that any very ample line bundle on a projective toric variety is normally generated. As an application we show that any ample line bundle on a toric Calabi-Yau hypersurface is ...

We propose a novel whole brain fiber-to-DTI registration method and apply it to a clinical study of small vessel diseases. It deforms a manually annotated fiber model to diffusion tensor images of new subjects. Fiber trajectories and anatomically meaningful fiber bundles are automatically obtained by this registration. The free-form deformations are used to regularize the transformations at the...