Displaying similar documents to “Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces”

On compact Kähler surfaces

Nicholas Buchdahl (1999)

Annales de l'institut Fourier

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Without relying on the classification of compact complex surfaces, it is proved that every such surface with even first Betti number admits a Kähler metric and that a real form of the classical Nakai-Moishezon criterion holds on the surface.

A Nakai-Moishezon criterion for non-Kähler surfaces

Nicholas Buchdahl (2000)

Annales de l'institut Fourier

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A version of the classical Nakai-Moishezon criterion is proved for all compact complex surfaces, regardless of the parity of the first Betti number.

Hermitian spin surfaces with small eigenvalues of the Dolbeault operator

Bogdan Alexandrov (2004)

Annales de l'Institut Fourier

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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