Vector Bundles on Cones over Projective Schemes.
Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology
Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.
Vector bundles on non-Kaehler elliptic principal bundles
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.
Vector bundles on p-adic curves and parallel transport
Vector bundles on plane cubic curves and the classical Yang–Baxter equation
In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical -matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic -matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin’s classication and prove...
Vector Bundles on Projective 3-Space.
Vector bundles on the cone over a curve
Vector Bundles over Affine Surfaces.
Vector bundles over real algebraic surfaces and threefolds
Vector Fields and Chern Numbers.
Vector fields from locally invertible polynomial maps in ℂⁿ
Let (F₁,..., Fₙ): ℂⁿ → ℂⁿ be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by ∂/∂F₁,...,∂/∂Fₙ. Our main result is the following: if n-1 of the vector fields have complete holomorphic flows along the typical fibers of the submersion , then the inverse map exists. Several equivalent versions of this main hypothesis are given.
Vector fields on the Sato Grassmannian.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
Vector spaces of matrices of low rank and vector bundles on projective spaces: An addendum to a paper by Eisenbud and Harris.
Vectorial extensions of Jacobians
The universal vectorial extension of a curve is described in terms of the geometry of the curve.
Vektorbündel auf Kurven mit Singularitäten.
Vektorbündel auf Kurven und Darstellungen der algebraischen Fundamentalgruppe.
Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum.
Vektorraumbündel in der Nähe von exzeptionellen Unterräumen - das Modulproblem.
Vektorraumbündel in der Nähe von kompakten komplexen Unterräumen.
Versal deformation of Hopf surfaces.