Download Riemannsche Flachen by Klaus Lamotke PDF

By Klaus Lamotke

Die Theorie Riemannscher Flächen wird vom Autor als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären und zu erläutern. Viele Beispiele und Bilder, die in der historischen Entwicklung eine Rolle spielten, ergänzen die Darstellung. Wegen seiner Methodenvielfalt enthält das Buch gleichzeitig Einführungen in die Topologie (Fundamentalgruppe, Überlagerungen, Flächen), in die algebraische Geometrie (Kurven und ihre Singularitäten) und in die Potentialtheorie (Perron-Prinzip).

Das vorliegende Buch beruht auf Vorlesungen und Seminaren für Studenten mittlerer und höherer Semester im Anschluß an eine Einführung in die komplexe Funktionentheorie.

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Download Computational commutative algebra 1 by Martin Kreuzer PDF

By Martin Kreuzer

Bridges the present hole within the literature among thought and actual computation of Groebner bases and their functions. A accomplished advisor to either the idea and perform of computational commutative algebra, excellent to be used as a textbook for graduate or undergraduate scholars. includes tutorials on many topics that complement the cloth.

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Download Structural Aspects in the Theory of Probability: A Primer In by Herbert Heyer PDF

By Herbert Heyer

This publication makes a speciality of the algebraic-topological facets of likelihood thought, resulting in a much wider and deeper knowing of easy theorems, comparable to these at the constitution of continuing convolution semigroups and the corresponding methods with self sufficient increments. the tactic utilized in the environment of Banach areas and of in the neighborhood compact Abelian teams is that of the Fourier rework. This analytic instrument besides the proper elements of harmonic research makes it attainable to check sure houses of stochastic procedures in dependence of the algebraic-topological constitution in their country areas. Graduate scholars, academics and researchers could use the booklet as a primer within the thought of chance measures on teams and comparable constructions.

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Download Riemann-Roch Algebra (Grundlehren der mathematischen by William Fulton PDF

By William Fulton

In quite a few contexts of topology, algebraic geometry, and algebra (e.g. workforce representations), one meets the next scenario. One has contravariant functors okay and A from a undeniable type to the class of earrings, and a common transformation p: K--+A of contravariant functors. The Chern personality being the critical examination ple, we name the homomorphisms Px: K(X)--+ A(X) characters. Given f: X--+ Y, we denote the pull-back homomorphisms through and fA: A(Y)--+ A(X). As functors to abelian teams, okay and A can also be covariant, with push-forward homomorphisms and fA: A( X)--+ A(Y). frequently those maps don't trip with the nature, yet there's a component r f E A(X) such that the subsequent diagram is commutative: K(X) A(X) fK j J A okay( Y) ------p;-+ A( Y) The map within the best line is p x improved via r f. whilst such commutativity holds, we are saying that Riemann-Roch holds for f. this kind of formula was once first given via Grothendieck, extending the paintings of Hirzebruch to this kind of relative, functorial atmosphere. due to the fact then viii advent a number of different theorems of this Riemann-Roch kind have seemed. Un derlying almost all these there's a simple constitution having to do simply with easy algebra, autonomous of the geometry. One function of this monograph is to explain this algebra independently of any context, in order that it will probably serve axiomatically because the desire arises.

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Download Global Aspects of Complex Geometry by Fabrizio Catanese, Hélène Esnault, Alan Huckleberry, Klaus PDF

By Fabrizio Catanese, Hélène Esnault, Alan Huckleberry, Klaus Hulek, Thomas Peternell

This choice of surveys offers an outline of contemporary advancements in advanced Geometry. themes diversity from curve and floor concept via unique kinds in larger dimensions, moduli conception, Kahler geometry, and crew activities to Hodge idea and attribute p-geometry. Written through verified specialists this e-book is a needs to for mathematicians operating in complicated Geometry.

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