On the logarithmic Riemann-Hilbert correspondence.
On the Lüroth Semigroup of curves lying on a smooth quadric.
On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²
A complete characterization of the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² is given. Moreover, a characterization of a component of a polynomial automorphism of ℂ² (in terms of the Łojasiewicz exponent at infinity) is given.
On the Łojasiewicz exponent at infinity of real polynomials
Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing...
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 near the fibre of polynomial mappings
We give the formula expressing the Łojasiewicz exponent near the fibre of polynomial mappings in two variables in terms of the Puiseux expansions at infinity of the fibre.
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 main cojecture of Iwasawa theory for imaginary quadratic fields.
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 mappings of elliptic curves defined over into .
On the maximal unramified quotients of -adic étale cohomology groups and logarithmic Hodge–Witt sheaves.
On the method of Coleman and Chabauty.
On the Milnor fibrations of weighted homogeneous polynomials
On the Milnor -groups of complete discrete valuation fields.
On the Minimal Models of Complex Manifolds.
On the minimal number of singular fibres in a family of surfaces of general type.
On the minimality of hyperplane sections of projective threefolds.
On the mini-superambitwistor space and super-Yang-Mills theory.
On the mixed Hodge structure associated to of a simply connected complex projective manifold