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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 241, Pages 122–131 (Mi tm392)  

This article is cited in 7 scientific papers (total in 7 papers)

Generalized Chisini's Conjecture

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (200 kB) Citations (7)
References:
Abstract: Chisini's Conjecture claims that a generic covering of the plane of degree $\geq 5$ is determined uniquely by its branch curve. A generalization (to the case of normal surfaces) of Chisini's Conjecture is formulated and considered. The generalized conjecture is checked in the following two cases: when the maximum of degrees of two generic coverings $\geq 12$ and when it $\leq 4$. Conditions on the number of singular points of a cuspidal curve $B$ necessary for $B$ to be the branch curve of a generic covering of given degree are found. In particular, it is shown that, if $B$ is a pure cuspidal curve (i.e. all its singular points are ordinary cusps), then $B$ can be the branch curve only of a generic covering of degree $\leq 5$.
Received in December 2002
Bibliographic databases:
Document Type: Article
UDC: 512.7
Language: Russian
Citation: Vik. S. Kulikov, “Generalized Chisini's Conjecture”, Number theory, algebra, and algebraic geometry, Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich, Trudy Mat. Inst. Steklova, 241, Nauka, MAIK «Nauka/Inteperiodika», M., 2003, 122–131; Proc. Steklov Inst. Math., 241 (2003), 110–119
Citation in format AMSBIB
\Bibitem{Kul03}
\by Vik.~S.~Kulikov
\paper Generalized Chisini's Conjecture
\inbook Number theory, algebra, and algebraic geometry
\bookinfo Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 241
\pages 122--131
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm392}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2024048}
\zmath{https://zbmath.org/?q=an:1078.14017}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 241
\pages 110--119
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  • This publication is cited in the following 7 articles:
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