کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8905199 1633782 2017 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On finite regular and holomorphic mappings
ترجمه فارسی عنوان
در مقادیر منظم و هولومورفیک محدود است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
We show that for every hypersurface V⊂Y and every k∈N, there are only a finite number of non-equivalent finite regular mappings f:X→Y such that the discriminant D(f) equals V and μ(f)=k. In particular if Knr={x∈Cn:∏i=1rxi=0} and X is a smooth and simply connected algebraic manifold, then every finite regular mapping f:X→Cn with D(f)=Knr is equivalent to one of the mappings fd1,…,dr:Cn∋(x1,…,xn)↦(x1d1,…,xrdr,xr+1,…,xn)∈Cn. Moreover, we obtain generalizations of the Lamy Theorem. We prove the same statement in the local (and sometimes global) holomorphic situation. In particular we show that if f:(Cn,0)→(Cn,0) is a proper and holomorphic mapping of topological degree two, then there exist biholomorphisms Ψ,Φ:(Cn,0)→(Cn,0) such that Ψ∘f∘Φ(x1,x2,…,xn)=(x12,x2,…,xn). Moreover, for every proper holomorphic mapping f:(Cn,0)→(Cn,0) which has a discriminant with only simple normal crossings, there exist biholomorphisms Ψ,Φ:(Cn,0)→(Cn,0) such that Ψ∘f∘Φ(x1,x2,…,xn)=(x1d1,x2d2,…,xrdr,xr+1,…,xn), where r is the number of irreducible components of the discriminant at 0.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 306, 14 January 2017, Pages 1377-1391
نویسندگان
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