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Enriques Surfaces I

This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approa...

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Bibliographic Details
Main Authors: Cossec, F., Dolgachev (Author)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 1989, 1989
Edition:1st ed. 1989
Series:Progress in Mathematics
Subjects:
Several Complex Variables And Analytic Spaces
Algebraic Geometry
Functions Of Complex Variables
Algebra
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 0. Preliminaries
  • S1. Double covers
  • S2. Rational double points
  • S3. Del Pezzo surfaces
  • S4. Symmetric quartic Del Pezzo surfaces
  • S5. Symmetric cubic Del Pezzo surfaces
  • S6. Prym canonical maps
  • S7. The Picard scheme
  • Bibliographical notes
  • I. Enriques surfaces: generalities
  • S1. Classification of algebraic surfaces
  • S2. The Picard group
  • S3. The K3-cover
  • S4. Differential invariants
  • S5. Riemann-Roch and a vanishing theorem
  • S6. Examples
  • Bibliographical notes
  • II. Lattices and root bases
  • S1. Generalities
  • S2. Root bases and their Weyl groups
  • S3. Root bases of finite and affine type
  • S4. Root bases of hyperbolic type
  • S5. The Enriques lattice
  • S6. The Reye lattice
  • S7. The function ?M
  • S8. 2-congruence subgroups of finite Weyl groups
  • S9. The factor group W/W(2)
  • S10. The structure of W(2)
  • Bibliographical notes
  • Tables
  • III. The geometry of the Enriques lattice.
  • S1. Divisors of canonical type
  • S2. The nodal chamber
  • S3. Canonical r-sequences and U[r]-markings
  • S4. U-markings
  • S5. U[3]-markings
  • S6. Linear systems /C/ with C2 ? 10
  • Bibliographical notes
  • IV. Projective models.
  • S1. Preliminaries
  • S2. Linear systems on K3-surfaces
  • S3. Numerical connectedness
  • S4. Base-points
  • S5. Hyperelliptic maps
  • S6. Birational maps
  • S7. Superelliptic maps
  • S8. The branch locus of superelliptic maps
  • S9. Projective models of degree ?10
  • S10. Applications to linear systems
  • Appendix. A theorem of Igor Reider
  • Bibliographical notes
  • V. Genus 1 fibrations.
  • S1. Genus 1 fibrations:generalities
  • S2. The Picard group
  • S3. Jacobian fibrations
  • S4. Ogg-Shafarevich theory
  • S5. Weierstrass models
  • S6. Genus 1 fibrations on rational surfaces
  • S7. Genus 1 fibrations on Enriques surfaces
  • Bibliographical notes
  • Glossary ofnotations

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