R. Narasimhan

Compact Riemann Surfaces (eBook, PDF)

• Format: PDF

Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 122
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034886178
• Artikelnr.: 53086058

Inhaltsangabe

1. Algebraic functions.- 2. Riemann surfaces.- 3. The sheaf of germs of holomorphic functions.- 4. The Riemann surface of an algebraic function.- 5. Sheaves.- 6. Vector bundles, line bundles and divisors.- 7. Finiteness theorems.- 8. The Dolbeault isomorphism.- 9. Weyl's lemma and the Serre duality theorem.- 10. The Riemann-Roch theorem and some applications.- 11. Further properties of compact Riemann surfaces.- 12. Hyperelliptic curves and the canonical map.- 13. Some geometry of curves in projective space.- 14. Bilinear relations.- 15. The Jacobian and Abel's theorem.- 16. The Riemann theta function.- 17. The theta divisor.- 18. Torelli's theorem.- 19. Riemann's theorem on the singularities of ?.