TY  - BOOK
AU  - Harder, Gunter
TI  - Lectures on algebraic geometry I : : sheaves, cohomology of sheaves, and applications to riemann surfaces
T2  -  Aspects of mathematics. E ; 
SN  - 9783834818447
U1  - 512.7 
PY  - 2011///
CY  - Wiesbaden
PB  - Vieweg+Teubner Verlag, 
KW  -  Geometry, Algebraic
KW  - Algebraic topology
KW  - Sheaf theory
KW  - Riemann surfaces
KW  - Surfaces, Riemann
KW  - Sheaf cohomology
KW  - Sheaves (Algebraic topology)
KW  - Algebraische Geometrie
KW  - Garbe (Math.)
KW  - Homologische Algebra
KW  - Kohomologie
KW  - Kommutative Algebra
KW  - Komplexe Analysis
N1  - Includes bibliographical references and index
N2  - This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.
In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II
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UR  - https://link.springer.com/book/10.1007/978-3-8348-8330-8#about-book-reviews
ER  -