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Janusz Adamus

  1. A degree condition for maximal cycles in bipartite digraphs.

    Чт, 01/27/2011 - 16:01 — SomNambul
    Authors: Janusz Adamus, Lech Adamus
    Subjects: Combinatorics
    Abstract

    We prove a sharp Ore-type criterion for hamiltonicity of balanced bipartite
    digraphs: A bipartite digraph D, with colour classes of cardinality N, is
    hamiltonian if, for every pair of vertices u and v from opposite colour classes
    of D such that the arc u->v is not in D, the sum of the positive half-degree of
    u and the negative half-degree of v is greater than or equal to N+2.

  2. Tameness of complex dimension in real analytic sets.

    Ср, 06/23/2010 - 15:01 — SomNambul
    Authors: Janusz Adamus, Rasul Shafikov, Serge Randriambololona
    Subjects: Complex Variables
    Abstract

    Given a real analytic set X in a complex manifold and a positive integer d,
    denote by A(d) the set of points p in X at which there exists a germ of a
    complex analytic set of dimension d contained in X. It is proved that A(d) is a
    closed semianalytic subset of X.

  3. Geometric Auslander criterion for flatness.

    Пт, 09/04/2009 - 12:10 — SomNambul
    Authors: Janusz Adamus, Edward Bierstone, Pierre D. Milman
    Subjects: Algebraic Geometry
    Abstract

    Our aim is to understand the algebraic notion of flatness in explicit
    geometric terms. Let Y be a scheme of finite type over a perfect field, and let
    f:X->Y denote a morphism of schemes that is locally of finite type. We show
    that, if Y is regular, then nonflatness of f is equivalent to a severe
    discontinuity of the fibres - the existence of an associated component (perhaps
    embedded) at a point of the source whose image is nowhere dense in Y - after
    passage to the n'th fibred-power of f, where n = dim Y.

  4. Geometric Auslander criterion for flatness of an analytic mapping.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Janusz Adamus, Edward Bierstone, Pierre D. Milman
    Subjects: Commutative Algebra
    Abstract

    We prove that, if F is a coherent sheaf of modules over the source of a
    morphism f:X->Y of complex-analytic spaces, where Y is smooth, then the stalk
    of F at a point x in X is flat over R, the local ring of the target at f(x) if
    and only if the n-fold analytic tensor power of this stalk over R (where n =
    dim R) has no vertical elements. The result implies that if F is a finite
    module over a morphism f:X->Y of complex algebraic varieties, where Y is smooth
    and n=dim Y, then the stalk of F at x is R-flat if and only if its n-fold
    tensor power is a torsionfree R-module.

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