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pro vyhledávání: '"Kulikov, Vik S."'
Autor:
Kulikov, Vik. S.
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, 2023.
Comment: 10 pages, 4 figures
Comment: 10 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2306.10481
Autor:
Kulikov, Vik. S.
It is proved that the braid monodromy group $\Gamma_{P(z)}$ of a polynomial $P(z)\in\mathbb C[z]$, $\deg P(z)=n$, is the braid group $\text{Br}_n$ if the polynomial $P(z)$ has $n-1$ distinct critical values.
Comment: 7 pages, Fig. 2 is corrected
Comment: 7 pages, Fig. 2 is corrected
Externí odkaz:
http://arxiv.org/abs/2008.05187
Autor:
Kulikov, Vik. S.
In \cite{K-rig}, a map $\beta:\mathcal R\to\mathcal{B}el$ from the set $\mathcal R$ of equivalence classes of rigid germs of finite morphisms branched in germs of curves having $ADE$ singularity types onto the set $\mathcal{B}el$ of rational Belyi pa
Externí odkaz:
http://arxiv.org/abs/2008.05183
Autor:
Kulikov, Vik. S.
We prove that a germ of a finite morphism of smooth surfaces is rigid if the germ of its branch curve has one of $ADE$-singularity types and establish a correspondence between the set of rigid germs and the set of Belyi rational functions $f\in \bar{
Externí odkaz:
http://arxiv.org/abs/1911.10848
Autor:
Kulikov, Vik. S.
Questions related to deformations of germs of finite morphisms of smooth surfaces are discussed. A classification of the four-sheeted germs of finite covers $F: (U,o')\to (V,o)$ is given up to smooth deformations, where $(U,o')$ and $(V,o)$ are two c
Externí odkaz:
http://arxiv.org/abs/1812.03287
Autor:
Kulikov, Vik. S.
A finite morphism $f:X\to \mathbb P^2$ of a a smooth irreducible projective surface $X$ is called an almost generic cover if for each point $p\in \mathbb P^2$ the fibre $f^{-1}(p)$ is supported at least on $deg(f)-2$ distinct points and $f$ is ramifi
Externí odkaz:
http://arxiv.org/abs/1812.01313
Autor:
Kulikov, Vik. S.
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 giv
Externí odkaz:
http://arxiv.org/abs/1810.01705
Autor:
Kulikov, Vik. S.
We prove that for a generic Lefschetz pencil of plane curves of degree $d\geq 3$ there exists a curve $H$ (called the Hesse curve of the pencil) of degree $6(d-1)$ and genus $3(4d^2-13d+8)+1$, and such that: $(i)$ $H$ has $d^2$ singular points of mul
Externí odkaz:
http://arxiv.org/abs/1704.01417
Autor:
Kulikov, Vik S.
We prove that the monodromy group of the inflection points of plane curves of degree $d$ is the symmetric group $\mathbb S_{3d(d-2)}$ for $d\geq 4$ and in the case $d=3$ this group is the group of the projective transformations of $\mathbb P^2$ leavi
Externí odkaz:
http://arxiv.org/abs/1703.10430
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