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Displaying similar documents to “Finite extensions of mappings from a smooth variety”

Fragmented deformations of primitive multiple curves

Jean-Marc Drézet (2013)

Open Mathematics

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A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also...

On extremal mappings in complex ellipsoids

Armen Edigarian (1995)

Annales Polonici Mathematici

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Using a generalization of [Pol] we present a description of complex geodesics in arbitrary complex ellipsoids.

On π -metrizable spaces, their continuous images and products

Derrick Stover (2009)

Commentationes Mathematicae Universitatis Carolinae

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A space X is said to be π -metrizable if it has a σ -discrete π -base. The behavior of π -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly d -separable spaces as those which are the image of a π -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a π -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a π -metrizable topological group must be metrizable...

A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially S r , s -graphic

Jian Hua Yin (2012)

Czechoslovak Mathematical Journal

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The split graph K r + K s ¯ on r + s vertices is denoted by S r , s . A non-increasing sequence π = ( d 1 , d 2 , ... , d n ) of nonnegative integers is said to be potentially S r , s -graphic if there exists a realization of π containing S r , s as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for π to be potentially S r , s -graphic. They are extensions of two theorems due to A. R. Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes...

The set of points at which a polynomial map is not proper

Zbigniew Jelonek (1993)

Annales Polonici Mathematici

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We describe the set of points over which a dominant polynomial map f = ( f 1 , . . . , f n ) : n n is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by ( i = 1 n d e g f i - μ ( f ) ) / ( m i n i = 1 , . . . , n d e g f i ) .

Uniformly convex functions II

Wancang Ma, David Minda (1993)

Annales Polonici Mathematici

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses f - 1 ( w ) = w + d w ² + d w ³ + . . . . The series expansion for f - 1 ( w ) converges when | w | < ϱ f , where 0 < ϱ f depends on f. The sharp bounds on | a n | and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on | a n | and all extremal functions for...