Algebraic Curves and One-dimensional Fields

Erscheinungsjahr 2002
ISBN: 978-0-8218-2862-5
Verlag: American Mathematical Society

Buch, Englisch, Band 8, Format (B × H): 179 mm x 255 mm, Gewicht: 399 g

Reihe: Courant Lecture Notes

This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. It demonstrates how curves can act as a natural introduction to algebraic geometry.

Algebraic curves have many special properties that make their study particularly rewarding. As a result, curves provide a natural introduction to algebraic geometry. In this book, the authors also bring out certain aspects of curves and emphasize connections with algebra. This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. The authors make a point of using concrete examples and explicit methods to ensure that the style is clear and understandable. Several chapters develop the connections between the geometry of algebraic curves and the algebra of one-dimensional fields. This is an interesting topic that is rarely found in introductory texts on algebraic geometry.

Algebraic Preliminaries. From algebra to geometry. Geometry of dimension one. Divisors and line bundles. Vector bundles, coherent sheaves, and cohomology. Vector bundles on mathbb{P}{1}. General theory of curves. Elliptic curves. The Riemann-Roch theorem. Curves over arithmetic fields. Bibliography. Index

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Über Autor(innen)

(both of The Courant Institute of Mathematical Sciences, New York University, USA)