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Hermitian spin surfaces with small eigenvalues of the Dolbeault operator

Bogdan Alexandrov (2004)

Annales de l'Institut Fourier

We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples

Hermitian-Einstein Connections and Stable Vector Bundles Over Compact Complex Surfaces.

N.P. Buchdahl (1988)

Mathematische Annalen

Higher de Rham-Witt complexes of supersingular K3 surfaces

Niels O. Nygaard (1980)

Compositio Mathematica

Holomorphic Automorphisms of Compact Kähler Surfaces and Their Induced Actions in Cohomology.

C.A.M. Peters (1979)

Inventiones mathematicae

Holomorphic Conformal Structures and Uniformization of Complex Surfaces.

Isao Naruki, Ryoichi Kobayashi (1987/1988)

Mathematische Annalen

Holomorphic Projective Structures on Compact Complex Surfaces. II.

Takushiro Ochiai, Shoshichi Kobayashi (1981)

Mathematische Annalen

Holomorphic Projective Structures on Compact Complex Surfaces.

Takushiro Ochiai, Shoshichi Kobayashi (1980)

Mathematische Annalen

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

Homotopieklassifikation einfach zusammenhängender normaler kompakter komplexer Flächen.

Ludger Kaup, Gottfried Barthel (1974)

Mathematische Annalen

Hyperbolicity properties of quotient surfaces by freely operating arithmetic lattices

Eberhard Oeljeklaus, Christina Schmerling (2000)

Annales de l'institut Fourier

Let $D$ be a bounded symmetric domain in $ℂ^{2}$ and $Γ \subset {Aut}^{0} D$ an irreducible arithmetic lattice which operates freely on $D$ . We prove that the cusp–compactification $\overline{X}$ of $X = D / Γ$ is hyperbolic.

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