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Title Details:
Algebraic curves
Other Titles: An Introduction to algebraic geometry
Authors: Kontogeorgis, Aristides
Antoniadis, Ioannis
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > ARITHMETIC ALGEBRAIC GEOMETRY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ALGEBRAIC GEOMETRY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ALGEBRAIC GEOMETRY > CURVES
Keywords:
Algebraic curves
Schemes
Algebraic geometry
Riemann surfaces
Description:
Abstract:
The starting point for algebraic geometry was the study of algebraic sets, that is the study of the locus of points satisfying a set of polynomial equations. The geometric properties of such sets are encoded inside the rings of functions that are naturally defined on such sets. In this book we develop both the more abstract theory of schemes and the classical approach in terms of Riemann surfaces and algebraic function fields over a field of arbitrary characteristic.
Linguistic Editors: Kalliaras, Dimitrios
Technical Editors: Kontogeorgis, Aristides
Type: Undergraduate textbook
Creation Date: 2021
Item Details:
ISBN 978-618-85370-1-9
License: Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0)
DOI http://dx.doi.org/10.57713/kallipos-10
Handle http://hdl.handle.net/11419/8009
Bibliographic Citation: Kontogeorgis, A., & Antoniadis, I. (2021). Algebraic curves [Undergraduate textbook]. Kallipos, Open Academic Editions. http://dx.doi.org/10.57713/kallipos-10
Language: Greek
Consists of:
1. Affine algebraic sets
2. Projective varieties
3. Schemes
4. Categories and schemes
5. Elements of algebraic topology
6. Elements of sheaf cohomology
7. Compact Riemann surfaces
8. Algebraic function fields
9. Moduli spaces and deformation theory
10. Appendix
Publication Origin: Kallipos, Open Academic Editions