Kähler manifolds with numerically effective Ricci class
Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
Let be a compact Kähler manifold and be a -divisor with simple normal crossing support and coefficients between and . Assuming that is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on having mixed Poincaré and cone singularities according to the coefficients of . As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair .
K-analytic versus ccm-analytic sets in nonstandard compact complex manifolds
It is shown that in an elementary extension of a compact complex manifold M, the K-analytic sets (where K is the algebraic closure of the underlying real closed field) agree with the ccm-analytic sets if and only if M is essentially saturated. In particular, this is the case for compact Kähler manifolds.
Killing divisor classes by algebraisation
It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.
Komplexe Basen zu quasieigentlichen holomorphen Abbildungen
Kuranishi families for Hopf surfaces