Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths

Geometry of Algebraic Curves

Volume II with a contribution by Joseph Daniel Harris
Mitarbeit:Harris, Joseph Daniel

• Broschiertes Buch

Produktbeschreibung

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source.

The first volume appeared 1985 as vol. 267 of the same series.

Produktdetails

• Grundlehren der mathematischen Wissenschaften 268
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-662-50620-2
• Softcover reprint of the original 1st ed. 2011
• Seitenzahl: 996
• Erscheinungstermin: 23. August 2016
• Englisch
• Abmessung: 235mm x 155mm x 53mm
• Gewicht: 1496g
• ISBN-13: 9783662506202
• ISBN-10: 3662506203
• Artikelnr.: 48941340

Inhaltsangabe

Preface.- Guide to the Reader.- Chapter IX. The Hilbert Scheme.- Chapter X. Nodal curves.- Chapter XI. Elementary deformation theory and some applications.- Chapter XII. The moduli space of stable curves.- Chapter XIII. Line bundles on moduli.- Chapter XIV. The projectivity of the moduli space of stable curves.- Chapter XV. The Teichmüller point of view.- Chapter XVI. Smooth Galois covers of moduli spaces.- Chapter XVII. Cycles on the moduli spaces of stable curves.- Chapter XVIII. Cellular decomposition of moduli spaces.- Chapter XIX. First consequences of the cellular decomposition .- Chapter XX. Intersection theory of tautological classes.- Chapter XXI. Brill-Noether theory on a moving curve.- Bibliography.- Index.

Rezensionen

From the reviews: "A comprehensive account of the deepest results of the geometry of algebraic curves that were obtained in the second half of the 20th century using some of the more advanced techniques of abstract algebraic geometry ... . at the end of every chapter there bibliographical notes that guide the reader to the original literature and further developments and sets of exercises that complement the theory ... . an immediate standard reference for researchers and students working on the geometry of algebraic curves ... ." (Felipe Zaldivar, The Mathematical Association of America, July, 2011)