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Birkhäuser

Moduli of Weighted Hyperplane Arrangements

  • Textbook
  • © 2015

Overview

Authors:
  1. Valery Alexeev

    1. Department of Mathematics, University of Georgia, Athens, USA

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Editors:
  1. Gilberto Bini

    1. Università degli Studi di Milano, Milano, Italy

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  2. Martí Lahoz

    1. Université Paris Diderot, Paris, France

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  3. Emanuele Macrí

    1. Department of Mathematics, Northeastern University, Boston, USA

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  4. Paolo Stellari

    1. Università degli Studi di Milano, Milano, Italy

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  • Develops concrete examples
  • Features specific interplay between various areas in Algebraic Geometry
  • Focusses on the higher-dimensional case
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
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  2. Stable Pairs and Their Moduli

    • Valery Alexeev
    Pages 3-22

  3. Stable Toric Varieties

    • Valery Alexeev
    Pages 23-41

  4. Matroids

    • Valery Alexeev
    Pages 43-58

  5. Matroid Polytopes and Tilings

    • Valery Alexeev
    Pages 59-74

  6. Weighted Stable Hyperplane Arrangements

    • Valery Alexeev
    Pages 75-92

  7. Abelian Galois Covers

    • Valery Alexeev
    Pages 93-100

  8. Back Matter

    Pages 101-105
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Keywords

About this book

This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements (shas).

Authors, Editors and Affiliations

  • Università degli Studi di Milano, Milano, Italy

    Gilberto Bini, Paolo Stellari

  • Université Paris Diderot, Paris, France

    Martí Lahoz

  • Department of Mathematics, Northeastern University, Boston, USA

    Emanuele Macrí

  • Department of Mathematics, University of Georgia, Athens, USA

    Valery Alexeev

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