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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 241, Pages 122–131
(Mi tm392)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/tm392 https://www.mathnet.ru/eng/tm/v241/p122
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