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Titlebook: Ball and Surface Arithmetics; Rolf-Peter Holzapfel Textbook 1998 Springer Fachmedien Wiesbaden 1998 algebra.algorithms.classification.fiel

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期刊全称Ball and Surface Arithmetics
影响因子2023Rolf-Peter Holzapfel
视频video
学科分类Aspects of Mathematics
图书封面Titlebook: Ball and Surface Arithmetics;  Rolf-Peter Holzapfel Textbook 1998 Springer Fachmedien Wiesbaden 1998 algebra.algorithms.classification.fiel
影响因子This monograph is based on the work of the author on surface theory con­ nected with ball uniformizations and arithmetic ball lattices during several years appearing in a lot of special articles. The first four chapters present the heart of this work in a self-contained manner (up to well-known ba­ sic facts) increased by the new functorial concept of orbital heights living on orbital surfaces. It is extended in chapter 6 to an explicit HURWITZ theory for CHERN numbers of complex algebraic surfaces with the mildest singularities, which are necessary for general application and proofs. The chapter 5 is dedicated to the application of results in earlier chapters to rough and fine classifications of PICARD modular surfaces. For this part we need additionally the arithmetic work of FEUSTEL whose final results are presented without proofs but with complete references. We had help­ ful connections with Russian mathematicians around VENKOV, VINBERG, MANIN, SHAFAREVICH and the nice guide line of investigations of HILBERT modular surfaces started by HIRZEBRUCH in Bonn. More recently, we can refer to the independent (until now) study of Zeta functions of PICARD modular surfaces in the book [
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Picard Modular Surfaces,we classify completely the corresponding surfaces in sections 1 and 2. These examples clarify the way of the . classification of . modular surfaces corresponding to K with higher discriminants. There are some new results for the . modular surfaces of . numbers which are of number theoretic interest
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,ℚ-Orbital Surfaces,xtend the notion of orbital surfaces. In the Galois theory orbital surfaces, orbital curves and points can be expressed by means of divisors and singularities. These are quite classical objects. The classical language does not work nicely in the general theory of surface coverings. Here we have to i
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978-3-322-90171-2Springer Fachmedien Wiesbaden 1998
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Handbuch der Laplace-TransformationWe work in the category of all compact complex normal algebraic surfaces with (at most) singularities of . type. A . on such a surface . is a formal sum ., where . = (., .; ...) is a (smooth) orbital curve on . and .. is an (arranged) abelian point on ., . = 1,...,., . = 1,..., .. The following axioms have to be satisfied:
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Abelian Points,We consider complex representations of finite groups . ., of rank 2.
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