54 citations · 133 across the 27 of their papers we have counts for
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On irreducible germs of generic morphisms
Vik. S. Kulikov
The article examines a set of irreducible germs of %finite generic morphisms to the projective plane whose branch curve germs …
Theorems of Chisini type
Vik. S. Kulikov
A text of the talk given by the author on Conference on Algebra, Algebraic Geometry and Number Theory dedicated to the 100th anniversary of I.R. Shafarevich, Moscow, June 5 -- 9, 2…
Rigid germs of finite morphisms of smooth surfaces and rational Belyi pairs
Vik. S. Kulikov
In \cite{K-rig}, a map from the set of equivalence classes of rigid germs of finite morphisms branched in germs of curves having s…
On rigid germs of finite morphisms of smooth surfaces
Vik. S. Kulikov
We prove that a germ of a finite morphism of smooth surfaces is rigid if the germ of its branch curve has one of -singularity types and establish a correspondence between the…
On germs of finite morphisms of smooth surfaces
Vik. S. Kulikov
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…
On the almost generic covers of the projective plane
Vik. S. Kulikov
A finite morphism of a a smooth irreducible projective surface is called an almost generic cover if for each point the fibre …
Amazing examples of nonrational smooth spectral surfaces
Viktor S. Kulikov, Alexander Zheglov
In this paper we construct first examples of smooth projective surfaces of general type satisfying the following conditions: there are 1) an ample integral curve with a…
The Hesse curve of a Lefschtz pencil of plane curves
Vik. S. Kulikov
We prove that for a generic Lefschetz pencil of plane curves of degree there exists a curve (called the Hesse curve of the pencil) of degree and genus $3(4d^…
On the monodromy of the inflection points of plane curves
Vik S. Kulikov
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…
On rigid plane curves
Viktor S. Kulikov, Eugenii Shustin
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective tra…
Duality of planar and spacial curves: new insight
Victor Kulikov, Eugenii Shustin
We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (deg…
The ambiguity index of an equipped finite group
F. A. Bogomolov, Vik. S. Kulikov
In \cite{Ku0}, the ambiguity index was introduced for each equipped finite group . It is equal to the number of connected components of a Hurwitz space parametri…
On the Galois groups of the dualizing coverings for plane curves
Vik. S. Kulikov
Let be an irreducible component of a reduced projective curve defined over the field , , and let be the set of l…
On numerically pluricanonical cyclic coverings
Viatcheslav Kharlamov, Viktor Kulikov
In this article, we investigate some properties of cyclic coverings of complex surfaces of general type branched along smooth curves that are numerically equivalent to a multiple o…
Covering semigroups
V. Kharlamov, Vik. Kulikov
We introduce and study a semigroup structure on the set of irreducible components of the Hurwitz space of marked coverings of a complex projective curve with given Galois group of…
A Remark on Classical Pluecker's formulae
Vik. S. Kulikov
For any reduced curve , we define the notions of the number of its virtual cusps and the number of its virtual nodes which are non-negative, coinc…
Factorization semigroups and irreducible components of Hurwitz space. II
Vik. S. Kulikov
This article is a continuation of the article with the same title (see arXiv:1003.2953v1). Let {\rm } be the Hurwitz space of degree covering…
Factorization semigroups and irreducible components of Hurwitz space
Vik. S. Kulikov
We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space…
On complete degenerations of surfaces with ordinary singularities in
V. S. Kulikov, Vik. S. Kulikov
We investigate the problem of existence of degenerations of surfaces in with ordinary singularities into plane arrangements in general position.
Automorphisms of Galois Coverings of Generic -Canonical Projections
V. Kharlamov, Vik. Kulikov
The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one o…
A remark on the non-rationality Problem for generic cubic fourfolds
Vik. S. Kulikov
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 o…
On Chisini's Conjecture. II
Vik. S. Kulikov
It is proved that if is a smooth projective surface and is a generic linear projection branched over a cuspidal curve $B\subset \mathbb…
Generic coverings of plane with A-D-E-singularities
V. S. Kulikov, Vik. S. Kulikov
We generalize results of the paper math.AG/9803144, in which Chisini's conjecture on the unique reconstruction of f by the curve B is investigated. For this fibre products of gener…
Braid Monodromy Factorization and Diffeomorphism Types
Vik. S. Kulikov, M. Teicher
In this manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this…