Displaying similar documents to “On compact Kähler surfaces”

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

Kähler-Einstein metrics singular along a smooth divisor

Raffe Mazzeo (1999)

Journées équations aux dérivées partielles

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In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor D . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical...