ON FINITE BRANCHED UNIFORMIZATIONS OF THE PROJECTIVE PLANE
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We give a brief survey of the so-called Fenchel's problem for the projective plane, that is the problem of existence of finite Galois coverings of the complex projective plane branched along a given divisor and prove the following result: Let p, q be two integers greater than 1 and C be an irreducible plane curve. If there is a surjection of the fundamental group of the complement of C into a free product of cyclic groups of orders p and q, then there is a finite Galois covering of the projective plane branched along C with any given branching index.
2015 ◽
Vol 159
(2)
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pp. 189-205
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2017 ◽
Vol 28
(02)
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pp. 1750013
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2018 ◽
Vol 97
(3)
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pp. 386-395
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2020 ◽
pp. 45-56
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2007 ◽
Vol 56
(2)
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pp. 931-946
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1997 ◽
Vol 40
(3)
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pp. 285-295
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