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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
** Edition: **
** Author(s): ** Alexei Skorobogatov
** Publisher: **
** Series: **
** Year: ** 2003
** Pages: ** 48
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: **
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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
** Divisors**

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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