Overview

The AMS has endeavored to publish and make available this succinct and quite elegant research monograph written by Field's Medalist and eminent researcher, Laurent Lafforgue. Lafforgue was the invited 2001-2002 Aisenstadt Chair at CRM. While acting in this capacity, he presented a seminar and a series of lectures. His material served as the cornerstone for this monograph. 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 Plucker embeddings, and toric varieties. The book is suitable for advanced graduate students and research mathematicians interested in the classification of moduli spaces.

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