Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 PDF Download

Author: J. W. S. Cassels
Publisher: Cambridge University Press
ISBN: 9780521483704
Category : Mathematics
Languages : en
Pages : 238

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A unique insight into the topic of curves of genus 2, by two of the world's leading practitioners.

Author: Viktoria Heu
Publisher: American Mathematical Soc.
ISBN: 1470435667
Category :
Languages : en
Pages : 103

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Book Description
The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

Author: G., van der Geer
Publisher: Springer Science & Business Media
ISBN: 1461204577
Category : Mathematics
Languages : en
Pages : 450

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Book Description
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Author: Kunihiko Kodaira
Publisher: CUP Archive
ISBN: 9780521217774
Category : Mathematics
Languages : en
Pages : 424

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Book Description
The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Author: George W. Boehlert
Publisher: Springer Science & Business Media
ISBN: 9401137927
Category : Science
Languages : en
Pages : 281

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Author: Charles Darwin
Publisher:
ISBN:
Category :
Languages : en
Pages : 712

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Author: Alexander Stoimenow
Publisher: CRC Press
ISBN: 1315362198
Category : Mathematics
Languages : en
Pages : 192

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In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.

Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 484

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Book Description
Contains the Society's Directory of members, , 1979-

Author: Roland Hayward
Publisher:
ISBN:
Category : Beetles
Languages : en
Pages : 112

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Author: Elbert Luther Little
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 60

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Book Description
A summary of the nomenclature and 22 distribution maps of subdivisions of the genus Pinus L., pine, are presented here to supplement Miscellaneous Publication 991--Geographic Distribution of the Pines of the world, with maps of 94 species. Important synonyms and lists of the species are included, and the slight changes in the classification of the subdivisions are explained. The maps of subdivisions combined from those of individual species show clearly and graphically the maximum natural range of all component species. These compiled maps of groups of related species may be useful in further researches, particularly in classification, geographical distribution, tree breeding and introduction, and evolution.