On the embedding of 1-convex manifolds with 1-dimensional exceptional sets.
On the finiteness theorem for rational maps on a variety of general type.
On the Kodaira Dimension of the Moduli Space of Curves.
On the length of the absolute Samuel stratum
On the Łojasiewicz Exponent near the Fibre of a Polynomial
The equivalence of the definitions of the Łojasiewicz exponent introduced by Ha and by Chądzyński and Krasiński is proved. Moreover we show that if the above exponents are less than -1 then they are attained at a curve meromorphic at infinity.
On the Łojasiewicz exponent of the gradient of a polynomial function
Let be a polynomial with complex coefficients. The Łojasiewicz exponent of the gradient of h at infinity is the least upper bound of the set of all real λ such that in a neighbourhood of infinity in ℂ², for c > 0. We estimate this quantity in terms of the Newton diagram of h. Equality is obtained in the nondegenerate case.
On the Mapping Problem for Algebraic Real Hypersurfaces.
On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions
In this paper, we show that if and are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if is a holomorphic mapping defined near a neighborhood of so that , then is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for mappings...
On the p-rank of an abelian variety and its endomorphism algebra.
Let A be an abelian variety defined over a finite field. In this paper, we discuss the relationship between the p-rank of A, r(A), and its endomorphism algebra, End0(A). As is well known, End0(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative field. Nevertheless, we give an example...
On the Spannedness and Very Ampleness of Certain Line Bundles on the Blow-ups of IP2C and Fr .
On the Structure of the Birational Abel Morphism.
On the theorem of de Franchis
On the transformation of unicursal surfaces
On unique and almost unique factorization of complete ideals II.
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.