Enrico Arbarello, Phillip Griffiths, Maurizio Cornalba

Geometry of Algebraic Curves

Volume II with a contribution by Joseph Daniel Harris
Mitarbeit:Arbarello, Enrico; Cornalba, Maurizio; Griffiths, Pillip A.

• Gebundenes 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.

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Grundlehren der mathematischen Wissenschaften 268
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 10078631, 978-3-540-42688-2
• 2011
• Seitenzahl: 996
• Erscheinungstermin: 4. April 2011
• Englisch
• Abmessung: 241mm x 160mm x 58mm
• Gewicht: 1780g
• ISBN-13: 9783540426882
• ISBN-10: 3540426884
• Artikelnr.: 14785521

Inhaltsangabe

From the contents:
Preface
Guide to the Reader
Chapter X. The Hilbert Scheme
Chapter XI. Nodal curves
Chapter XII. Elementary deformation theory and some applications
Chapter XIII. The moduli space of stable curves
Chapter XIV. Line bundles on moduli
Chapter XV. The projectivity of the moduli space of stable curves
Chapter XVI. The Teichmüller point of view
Chapter XVII. Smooth Galois covers of moduli spaces
Chapter XVIII. Cycles on the moduli spaces of stable curves
Chapter XIX. Cellular decomposition of moduli spaces
Chapter XX. First consequences of the cellular decomposition
Chapter XXI. Intersection theory of tautological classes
Chapter XXII. 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)