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alexei skorobogatov algebraic geometry [pdf]

Algebraic Geometry by Alexei Skorobogatov

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About this book :-
Algebraic Geometry written by Alexei Skorobogatov
This text introduce the basics of commutative algebra and algebraic geometry.

Book Detail :-
Title: Algebraic Geometry
Author(s): Alexei Skorobogatov
Year: 2003
Pages: 48
Type: PDF
Language: English
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About Author :-
The author Alexei Skorobogatov was born in Moscow, Russia but later he move to England. He completed his dissertation under the supervision of Yuri Manin, for which he was awarded a Ph.D. degree. He is interested in arithmetic and algebraic geometry, also cohomological approaches to rational points on algebraic varieties.

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Book Contents :-
Algebraic Geometry written by Alexei Skorobogatov cover the following topics. Basics of commutative algebra
Integral closure. Noetherian rings, Noether’s normalization and Nullstellensatz
Affine geometry
Zariski topology, Category of affine varieties, Examples of rational varieties, Smooth and singular points, Dimension. Application: Tsen’s theorem
Projective geometry
Projective varieties, Morphisms of projective varieties
Local geometry
Localization, local rings, DVR, Regular local rings, Geometric consequences of unique factorization in OP
The Picard group, Automorphisms of Pnk and of Ank, The degree of the divisor of a rational function on a projective curve, Bezout theorem for curves, Riemann–Roch theorem, From algebraic curves to error correcting codes
A More algebra
Krull’s intersection theorem, Completion, The topological space Spec(R)
B More geometry
Finite morphisms, Functoriality of Pic

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