In this paper we derive a list of all the possible indecomposable normalized rank–two vector bundles without intermediate cohomology on the prime Fano threefolds and on the complete intersection Calabi-Yau threefolds, say V , of Picard number ρ = 1. For any such bundle E, if it exists, we find the projective invariants of the curves C ⊂ V which are the zero–locus of general global sections of E...

An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we give a necessary and sufficient condition for a non-trivial line bundle OX(D) on X with |D| 6= ∅ and D 2 ≥ L − 6 to be an ACM and initialized line bundle with ...

We prove that the L metric on the direct image of an adjoint positive line bundle by a locally trivial submersion between projective manifolds is Nakano positive, under the assumption that the typical fiber has zero first Betti number. As a consequence, we get that the symmetric powers of an ample vector bundle tensorized by its determinant are Nakano positive, in particular Griffiths positive....

We calculate, at the classical level, the superpotential tri-linear couplings of the only known globally consistent heterotic minimal supersymmetric Standard Model [1]. This recently constructed model is based on a compactification of the E8 × E8 heterotic string theory on a Calabi-Yau threefold with Z2 fundamental group, coupled with a slope-stable holomorphic SU(5) vector bundle. In the obser...

We study, as hypersurfaces in toric varieties, elliptic Calabi–Yau fourfolds for F-theory compactifications dual to E8 × E8 heterotic strings compactified to four dimensions on elliptic Calabi–Yau threefolds with some choice of vector bundle. We describe how to read off the vector bundle data for the heterotic compactification from the toric data of the fourfold. This map allows us to construct...

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequen...

We consider C ⁎ -algebras constructed from compact group actions on complex vector bundles E → X endowed with a Hermitian metric. An action of G by isometries induces an the -correspondence Γ ( ) over consisting continuous sections, and associated Cuntz–Pimsner algebra O , so we can study crossed product ⋊ . If is free rank = n then prove that Morita–Rieffel equivalent to field Cuntz algebras o...

Homogeneous bundles on P2 = SL(3)/P can be described by representations of the parabolic subgroup P . In 1966 Ramanan proved that if ρ is an irreducible representation of P then the induced bundle Eρ on P 2 is simple and even stable (see [Ram]). Since P is not a reductive group, there is a lot of indecomposable reducible representations of P and to classify homogeneous bundles on P2 and among t...