Value Distribution Theory for Meromorphic Maps

✍ Scribed by Wilhelm Stoll (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 1985
• Tongue: English
• Leaves: 358
• Edition: 1
• Category: Library

✦ Synopsis

Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.

✦ Table of Contents

Front Matter....Pages I-XI
Introdution....Pages 1-91
Hermitian Geometry....Pages 92-114
Meromorphic Maps on Parabolic Manifolds....Pages 115-133
The First Main Theorem....Pages 134-150
Associated Maps....Pages 151-162
Frenet Frames....Pages 163-190
The Ahlfors Estimates....Pages 191-215
General Position....Pages 216-244
The Second Main Theroem....Pages 245-274
Value Distribution over a Function Field....Pages 275-309
An Example....Pages 310-316
The Theorem of Nevanlinna-Mori....Pages 317-333
References....Pages 334-343
Back Matter....Pages 344-347

✦ Subjects

Geography (general)