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Chirurgie des grassmanniennes
L. Lafforgue, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Monograph Series
2003; 170 pp; hardcover
Volume: 19
ISBN-10: 0-8218-3358-8
ISBN-13: 978-0-8218-3358-2
List Price: US$49
Member Price: US$39.20
Order Code: CRMM/19
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The AMS now makes available this succinct and quite elegant research monograph written by Fields Medalist and eminent researcher, Laurent Lafforgue. The material is an outgrowth of Lafforgue's lectures and seminar at the Centre de Recherches Mathématiques (University of Montréal, QC, Canada), where he held the 2001-2002 Aisenstadt Chair.

In the book, he addresses an important recurrent theme of modern mathematics: the various compactifications of moduli spaces, which have a large number of applications. This book treats the case of thin Schubert varieties, which are natural subvarieties of Grassmannians. He was led to these questions by a particular case linked to his work on the Langlands program. In this monograph, he develops the theory in a more systematic way, which exhibits strong similarities with the case of moduli of stable curves.

Prerequisites are minimal and include basic algebraic geometry, and standard facts about Grassmann varieties, their Plücker embeddings, and toric varieties. The book is suitable for advanced graduate students and research mathematicians interested in the classification of moduli spaces.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students and researchers interested in algebra and algebraic geometry.

Reviews

"The author develops the whole theory around this specific compactification problem in an extremely systematic, detailed, rigorous, comprehensible and enlightening manner ... which makes this research monograph also a unique reference book for this particular topic ... of great importance in geometric classification, which is designed and accessible for experienced researchers ... a masterpiece of contemporary research in compactification theory, and a true delicacy for adepted specialists ... The actual significance and utility of the theory presented here will become manifest in the course of the further developments in this field of research."

-- Zentralblatt MATH

Table of Contents

  • Cellules de Schubert minces et espaces de configurations de matroïdes
  • Compactifications: Pavages de convexes entiers et recollement des cellules de Schubert minces
  • Étude de quelques familles simples de compactifications
  • Le fibré équivariant universel sur la variété torique des facettes des pavages
  • Variations de variétés projectives rationneles avec structures logarithmiques
  • Références bibliographiques
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