arXiv subjects

Vik. Kulikov

Publications and source records attributed to Vik. Kulikov.

4 recordsLinked to original sources

arXiv2012

Covering semigroups

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 the coverings and fixed ramification type. As application, we give new conditions on the ramification type that are sufficient for irreducibility of the Hurwitz spaces, suggest some bounds on the number of irreducibility components under certain more general conditions, and show that the number of irreducible components coincides with the number of topological classes of the coverings if the number of brunch points is big enough.

math.AG↗

arXiv2007

Automorphisms of Galois Coverings of Generic $m$-Canonical Projections

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 obtains, in dimensions one and two, serieses of specific actions of the symmetric groups $S_d$ on curves and surfaces not deformable to an action of $S_d$ which is not the full automorphism group. As an application, new DIF $\ne$ DEF examples for $G$-varieties in complex and real geometry are given.

math.AG↗

arXiv2005

Surfaces with DIF$\ne$DEF real structures

We study real Campedelli surfaces up to real deformations and exhibit a number of such surfaces which are equivariantly diffeomorphic but not real deformation equivalent.

math.AG↗

arXiv2002

Deformation inequivalent complex conjugated complex structures and applications

Here, we resume and broaden the results concerned which appeared in math.AG/0101098 and math.AG/0104021. We start from summing up our example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and which, moreover, has no homeomorphisms reversing the canonical class. Then, we construct several series of higher dimensional compact complex manifolds having the same property. We end with discussing applications to the Dif=Def problems, to the existence of diffeomorphic plane cuspidal curves non equivalent under equisingular deformations and to the existence of (deformation) non equivalent symplectic structures with opposite canonical classes.

math.AG↗