Huang, Xiaojun
Published in
Science in China Series A: Mathematics

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued.

Cheung, Wing-Sum Wong, Bun
Published in
Science in China Series A: Mathematics

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.

Zhang, Chaohui
Published in
Chinese Annals of Mathematics, Series B

Let S be a Riemann surface with genus p and n punctures. Assume that 3p−3+n > 0 and n ≥ 1. Let a be a puncture of S and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen...

Patrizio, Giorgio Spiro, Andrea
Published in
Advances in Mathematics

A ( bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point x o , so that: (a) it is a smooth solution on M ∖ { x o } to the Monge–Ampère equation ( d d c u ) n = 0 ; (b) x o is a singular point for u of logarithmic type and e u extends smoothly on the bl...

El Kacimi Alaoui, Aziz
Published in
Mathematische Annalen

In (Ann Sc ENS Sér 3 4:361–380, 1887) Guichard proved that, for any holomorphic function g on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb C}}$$\end{docume...

Ornea, Liviu Verbitsky, Misha
Published in
Mathematische Annalen

A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widetilde M}$$\end{document...

Fujiki, Akira Pontecorvo, Massimiliano
Published in
Mathematische Annalen

In this note we show that in a certain subfamily of the Kuranishi family of any half Inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semicontinuity of algebraic dimensions in any sense does not hold in general for families of compact non-Kähler manifolds. In the Käh...

MIYACHI, Hideki

Berndtsson, Bo
Published in
Mathematische Zeitschrift

This paper is a sequel to (Berndtsson in Ann Math 169:531–560, 2009). In that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth Kähler morphism, twisted with a semipositive line bundle. We proved that the curvature of a such vector bundles is always semipositive (in the sense of Nakano). ...

Tsuboi, Shoji