2,759 research outputs found
Alexander modules of irreducible -groups
A complete description of the Alexander modules of knotted -manifolds in
the sphere , , and irreducible Hurwitz curves is given. This
description is applied to investigate properties of the first homology groups
of cyclic coverings of the sphere and the projective complex plane
branched respectively alone knotted -manifolds and
along irreducible Hurwitz (in particular, algebraic) curves.Comment: 44 page
A remark on the non-rationality Problem for generic cubic fourfolds
It is proved that the non-rationality of a generic cubic fourfold follows
from a conjecture on the non-decomposability in the direct sum of non-trivial
polarized Hodge structures of the polarized Hodge structure on transcendental
cycles on a projective surface.Comment: 9 page
On the almost generic covers of the projective plane
A finite morphism of a a smooth irreducible projective
surface is called an almost generic cover if for each point the fibre is supported at least on distinct points
and is ramified with multiplicity two at a generic point of its
ramification locus . In the article, the singular points of the branch curve
of an almost generic cover are investigated and main
invariants of the covering surface are calculated in terms of invariants of
the curve .Comment: 13 pages. Submitted to the Pure and Applied Math. Quarterl
Jacobian Conjecture and Nilpotent Mappings
We prove the equivalence of the Jacobian Conjecture (JC(n)) and the
Conjecture on the cardinality of the set of fixed points of a polynomial
nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).Comment: 10 pages, LaTeX2
On the monodromy of the inflection points of plane curves
We prove that the monodromy group of the inflection points of plane curves of
degree is the symmetric group for and in
the case this group is the group of the projective transformations of
leaving invariant the nine inflection points of the Fermat curve
of degree three.Comment: 19 page
On a Chisini Conjecture
Chisini's conjecture asserts that for a cuspidal curve
a generic morphism of a smooth projective surface onto of
degree , branched along , is unique up to isomorphism. We prove that
if is greater than the value of some function depending on the degree,
genus, and number of cusps of , then the Chisini conjecture holds for .
This inequality holds for many different generic morphisms. In particular, it
holds for a generic morphism given by a linear subsystem of the th canonical
class for almost all surfaces with ample canonical class.Comment: 28 pages, LaTeX2
On Chisini's Conjecture. II
It is proved that if is a smooth projective surface
and is a generic linear projection branched over a
cuspidal curve , then the surface is determined
uniquely up to an isomorphism of by the curve .Comment: 14 page
Factorizations in finite groups
A necessary condition for uniqueness of factorizations of elements of a
finite group with factors belonging to a union of some conjugacy classes of
is given. This condition is sufficient if the number of factors belonging
to each conjugacy class is big enough. The result is applied to the problem on
the number of irreducible components of the Hurwitz space of degree marked
coverings of with given Galois group and fixed collection of
local monodromies.Comment: 29 page
On germs of finite morphisms of smooth surfaces
Questions related to deformations of germs of finite morphisms of smooth
surfaces are discussed. A classification of the four-sheeted germs of finite
covers is given up to smooth deformations, where
and are two connected germs of smooth complex-analytic surfaces. The
singularity types of their branch curves and the local monodromy groups are
investigated also.Comment: Definition of D-automorphisms and several misprints are correcte
On the variety of the inflection points of plane cubic curves
In the paper, we investigate properties of the nine-dimensional variety of
the inflection points of the plane cubic curves. The description of local
monodromy groups of the set of inflection points near singular cubic curves is
given. Also, it is given a detailed description of the normalizations of the
surfaces of the inflection points of plane cubic curves belonging to general
two-dimensional linear systems of cubic curves, The vanishing of the
irregularity a smooth manifold birationally isomorphic to the variety of the
inflection points of the plane cubic curves is proved.Comment: 27 page
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