1998/03/29 by Вик. С. Куликов, Vik. S. Kulikov, Kulikov, Vik. S.
Mathematics · #14J99 (Primary) 14H10 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14H10 #msc:14J99
paper · pdf · doi:10.48550/arxiv.math/9803144
28 pages, LaTeX2e
arxiv created 1998/03/29 · openalex publication_date 1998/03/29 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Chisini's conjecture asserts that for a cuspidal curve B⊂ \mathbb P2 a generic morphism f of a smooth projective surface onto \mathbb P2 of degree ≥ 5, branched along B, is unique up to isomorphism. We prove that if °f is greater than the value of some function depending on the degree, genus, and number of cusps of B, then the Chisini conjecture holds for B. This inequality holds for many different generic morphisms. In particular, it holds for a generic morphism given by a linear subsystem of the mth canonical class for almost all surfaces with ample canonical class.