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Displaying 841 – 860 of 1145

On the logarithmic Riemann-Hilbert correspondence.

Ogus, Arthur (2003)

Documenta Mathematica

On the Lüroth Semigroup of curves lying on a smooth quadric.

A. Ragusa, G. Paxia, G. Raciti (1992)

Manuscripta mathematica

On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ²

Jacek Chądzyński, Tadeusz Krasiński (1992)

Annales Polonici Mathematici

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

Ha Huy Vui, Pham Tien Son (2008)

Annales Polonici Mathematici

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

Grzegorz Skalski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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

Ha Huy Vui, Nguyen Hong Duc (2008)

Annales Polonici Mathematici

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

Andrzej Lenarcik (1999)

Annales Polonici Mathematici

Let $h = \sum h_{α β} X^{α} Y^{β}$ 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 ${| g r a d h (x, y) | \geq c | (x, y) |}^{λ}$ 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.

Karl Rubin (1988)

Inventiones mathematicae

On the Mapping Problem for Algebraic Real Hypersurfaces.

S.M. Webster (1977)

Inventiones mathematicae

On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions

Xiaojun Huang (1994)

Annales de l'institut Fourier

In this paper, we show that if $M_{1}$ and $M_{2}$ are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if $f$ is a holomorphic mapping defined near a neighborhood of $M_{1}$ so that $f (M_{1}) \subset M_{2}$ , then $f$ 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...