Author | Cossec, Franรงois R. author |
---|---|
Title | Enriques Surfaces I [electronic resource] / by Franรงois R. Cossec, Igor V. Dolgachev |
Imprint | Boston, MA : Birkhรคuser Boston, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3696-2 |
Descript | X, 402 p. online resource |
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 | 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 of notations