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Vector bundles on blown-up Hopf surfaces

Matei Toma (2012)

Open Mathematics

We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces.

Vector bundles on manifolds without divisors and a theorem on deformations

Georges Elencwajg, O. Forster (1982)

Annales de l'institut Fourier

We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.

Vector bundles on non-Kaehler elliptic principal bundles

Vasile Brînzănescu, Andrei D. Halanay, Günther Trautmann (2013)

Annales de l’institut Fourier

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 fields and foliations on compact surfaces of class VII 0

Georges Dloussky, Karl Oeljeklaus (1999)

Annales de l'institut Fourier

It is well-known that minimal compact complex surfaces with b 2 > 0 containing global spherical shells are in the class VII 0 of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces...

When does a Bounded Domain Cover a Projective Manifold? (Survey)

Kasparian, Azniv (1997)

Serdica Mathematical Journal

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and TechnologyThe present survey introduces in some classical properties of the universal coverings of the projective algebraic manifolds. All the results are non-original. A forthcoming note is...

Which 3-manifold groups are Kähler groups?

Alexandru Dimca, Alexander Suciu (2009)

Journal of the European Mathematical Society

The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then G must be finite—and thus belongs to the well-known list of finite subgroups of O ( 4 ) , acting freely on S 3 .

Currently displaying 381 – 400 of 403