The Calabi problem for Fano threefolds

著者

書誌事項

The Calabi problem for Fano threefolds

Carolina Araujo ... [et al.]

(London Mathematical Society lecture note series, 485)

Cambridge University Press, 2023

  • : pbk

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注記

Other authors: Ana-Maria Castravet, Ivan Cheltsov, Kento Fujita, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Süß, Nivedita Viswanathan

Includes bibliographical references (p. 430-439) and index

内容説明・目次

内容説明

Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kahler-Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kahler-Einstein metric, containing many additional relevant results such as the classification of all Kahler-Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.

目次

  • Introduction
  • 1. K-stability
  • 2. Warm-up: smooth del Pezzo surfaces
  • 3. Proof of main theorem: known cases
  • 4. Proof of main theorem: special cases
  • 5. Proof of main theorem: remaining cases
  • 6. The big table
  • 7. Conclusion
  • Appendix. Technical results used in proof of main theorem
  • References
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BD02877074
  • ISBN
    • 9781009193399
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    vii, 441 p.
  • 大きさ
    23 cm
  • 分類
  • 件名
  • 親書誌ID
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