The Moduli Space of Curves (Progress in Mathematics, 129, Band 129) - Hardcover

Buch 21 von 170: Progress in Mathematics
 
9780817637842: The Moduli Space of Curves (Progress in Mathematics, 129, Band 129)
Hardcover
ISBN 10: 0817637842 ISBN 13: 9780817637842
Verlag: Birkhäuser, 1995

Inhaltsangabe

This generalization of geometry is bound to have wide­ spread repercussions for mathematics as well as physics. The unearthing of it will entail a new golden age in the interaction of mathematics and physics. E. Witten (1986) The idea that the moduli space Mg of curves of fixed genus 9 - that is, the algebraic variety that parametrizes all curves of genus 9 - is an intriguing object in its own right seems to have come slowly. Although the para­ meters or moduli of curves surface in Riemann's famous memoir on abelian functions (from 1857) and in work of Hurwitz and later were considered by the geometers of the Italian school, for a long time they attracted attention only in the special case 9 = 1, where they were studied in the framework of the theory of modular functions. The work of Grothendieck, who in the early sixties pointed the way towards the right approach, and the subsequent construction (in 1965) of the moduli space Mg by Mumford were the first foundational work, to be followed by the construction of a compactification Mg by Deligne and Mumford in 1969. The theorem of Harris and Mumford saying that for 9 sufficiently large the space Mg is of general type was the first big insight in its structure.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science."

Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
1995
Sprache
Englisch
ISBN 10 
0817637842
ISBN 13 
9780817637842
Einband
Gebundene Ausgabe
Anzahl der Seiten
575
Herausgeber
Dijkgraaf Robert H., Faber Carel, Geer Gerard B.M. Van Der
Kontakt zum Hersteller
preigu GmbH & Co. KG
mail@preigu.de

Lengericher Landstr. 19
Osnabrück
Niedersachsen
49078
Deutschland

Weitere beliebte Ausgaben desselben Titels

9781461287148: The Moduli Space of Curves (Progress in Mathematics, Band 129)

Vorgestellte Ausgabe

ISBN 10:  1461287146 ISBN 13:  9781461287148
Verlag: Birkhäuser, 2011
Softcover