For any ample line bundle $L$ on a projective toric variety of dimension $n$, it is known that the line bundle $L^{\otimes i}$ is normally generated if $i$ is greater than or equal to $n-1$. We prove that $L^{\otimes i}$ is also normally presented if $i$ is greater than or equal to $n-1$. Furthermore we show that $L^{\otimes i}$ is normally presented for $i\ge [n/2]+1$ if $L$ is normally generated.

The smooth Fano threefolds with Picard number two in positive characteristic are classified. The each class has the same description as in characteristic zero. We give also a new example of Fano threefolds with Picard number three having a wild conic bundle structure.

We construct a pinching semiconjugacy from a quadratic polynomial $f_c(z)=z^2+c$ with $c \in (0, 1/4)$ to $f_{1/4}(z)=z^2+1/4$ on the sphere. By lifting this semiconjugacy to their natural extensions, we investigate the structure of the regular leaf space of $f_{1/4}$ in detail.

In this article we show several convergence and extension theorems for analytic hypersurfaces (not necessarily with normal crossings) and for closed pluripolar sets of complex manifolds. Moreover, a generalization of theorem of Alexander to complex spaces is given.

In this article an analogue of E. Cartan's theorem about the existence of (local) totally geodesic submanifolds with a prescribed tangent plane is proved, namely for the existence of spherically bent submanifolds (= extrinsic spheres); also a global version is deduced.

In this paper, some theorems of Picard type relating to the total derivative for entire functions of several complex variables are proved.

If we are given a $G$-manifold $M$, $G$ a finite abelian group of odd order, by taking fixed submanifolds $M^H$ for various subgroups $H$ of $G$, we obtain a family $(M^H)_{H \le G}$ of submanifolds of $M$. The Euler characteristics $\chi (M^H)$ of such submanifolds satisfy some congruence relations. Conversely, in this paper we show that if we are given a family $(N_i)$ of submanifolds $N_i$ of a manifold $N$ and if the Euler characteristics $\chi (N_i)$ satisfy some congruence relations, then, after adding some family, $(N_i)$ can be cut and pasted into a family obtained from a $G$-manifold.