On polarized canonical Calabi-Yau threefolds.
On polynomials whose fibres are irreducible with no critical points.
On surfaces with and non-birational bicanonical maps.
On the Adjunction Mapping.
On the adjunction theoretic classification of polarized varieties.
On the birational automorphism groups of algebraic varieties
On the curves through an general point of a smooth surface in IP3.
On the Diophantine equation ... (X, Y) = ... (x, y).
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