Displaying similar documents to “On sets of confluent and related mappings in the space Y X

Birational Finite Extensions of Mappings from a Smooth Variety

Marek Karaś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present an example of finite mappings of algebraic varieties f:V → W, where V ⊂ kⁿ, W k n + 1 , and F : k k n + 1 such that F | V = f and gdeg F = 1 < gdeg f (gdeg h means the number of points in the generic fiber of h). Thus, in some sense, the result of this note improves our result in J. Pure Appl. Algebra 148 (2000) where it was shown that this phenomenon can occur when V ⊂ kⁿ, W k m with m ≥ n+2. In the case V,W ⊂ kⁿ a similar example does not exist.

On a result by Clunie and Sheil-Small

Dariusz Partyka, Ken-ichi Sakan (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk 𝔻 , if F ( 𝔻 ) is a convex domain, then the inequality | G ( z 2 ) - G ( z 1 ) | < | H ( z 2 ) - H ( z 1 ) | holds for all distinct points z 1 , z 2 𝔻 . Here H and G are holomorphic mappings in 𝔻 determined by F = H + G ¯ , up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in and improve it provided F is additionally a quasiconformal mapping...

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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