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Lectures on Algebraic Geometry I [electronic resource] : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces / by Günter Harder.

By: Harder, Günter [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Aspects of Mathematics ; 35Publisher: Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2011Edition: 2nd revised EditionDescription: XIII, 301 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783834883308Subject(s): Mathematics | Algebra | Geometry | Mathematics | Geometry | AlgebraAdditional physical formats: Printed edition:: No titleDDC classification: 516 LOC classification: QA440-699Online resources: Click here to access online In: Springer eBooksSummary: 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.
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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.

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