Hodge theory and the local Torelli problem /

Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Tu, Loring W. (Auteur)
Format: Électronique eBook
Langue:Inglés
Publié: Providence, Rhode Island : American Mathematical Society, [1983]
Collection:Memoirs of the American Mathematical Society ; no. 279.
Sujets:
Curves, Algebraic.
Surfaces, Algebraic.
Hodge theory.
Torelli theorem.
Courbes algébriques.
Surfaces algébriques.
Théorie de Hodge.
Théorème de Torelli.
Curves, Algebraic
Hodge theory
Surfaces, Algebraic
Torelli theorem
Accès en ligne:Texto completo
Table des matières:
  • Table of Contents
  • Introduction
  • I. Variation of Hodge structure
  • 1. The period map
  • 2. The Hodge bundles in the smooth case
  • 3. The Hodge bundles when there are singular fibers
  • The log complex
  • Relative dualizing sheaf
  • The canonical extension
  • 4. A multiplicative formula for the holomorphic Euler characteristic
  • 5. Monodromy
  • 6. Mixed Hodge structures and the numerical invariants of a degeneration
  • 6.1. Varieties with normal crossings
  • 6.2. The limiting mixed Hodge structure
  • 6.3. The Clemens-Schmid exact sequence
  • 6.4. Genus of a singular curve.
  • II. Local Torelli for curves
  • 7. The case of no singular fibers
  • 8. With singular fibers
  • 8.1. First proof: mixed Hodge structure and the topology of the singular fiber
  • 8.2. Second proof: using the relative dualizing sheaf to map X into a projective space
  • 8.3. Third proof: the ample cone on the moduli space M
  • III. Local Torelli in higher dimensions
  • 9. Surfaces with large irregularity
  • 10. Threefolds and fourfolds with large irregularity
  • Bibliography
  • List of Notations
  • Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • K
  • L
  • M
  • N
  • P
  • Q
  • R
  • S
  • T.
  • U
  • V
  • W
  • Y.

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