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Ueda theory: theorems and problems

About this Title

Amnon Neeman

Publication: Memoirs of the American Mathematical Society
Publication Year: 1989; Volume 81, Number 415
ISBNs: 978-0-8218-2478-8 (print); 978-1-4704-0838-1 (online)
DOI: https://doi.org/10.1090/memo/0415
MathSciNet review: 990364
MSC: Primary 32E10; Secondary 14J15, 32J15

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Table of Contents

Chapters

  • Article 1. Geometric consequences of Ueda’s results
  • 0. Introduction
  • 1. The Ueda class
  • 2. Variation of the Ueda class
  • 3. The Ueda class and plurisubharmonic functions
  • 4. The proofs of Lemma 3.2 and Lemma 3.4
  • 5. The Ueda class of curves on projective surfaces
  • 6. The case of elliptic curves
  • 7. Sections of $\mathbb {P}^1$-bundles
  • 8. The functoriality of the Ueda class
  • 9. Ueda classes of high type
  • 10. A different example
  • Article 2. Problems in Ueda theory
  • 0. Introduction
  • 1. Infinitesimal connections
  • 2. Lifting infinitesimal connections
  • 3. The Ueda class
  • 4. Variation of the Ueda class
  • 5. The Ueda class of $M \subset X$ with a torsion normal bundle
  • 6. Classification
  • 7. Higher dimensions
  • 8. Computations of some Ueda classes
  • 9. Elliptic curves $M \subset X$ with $u(M,X)\neq 0$