Notes on Basic Algebraic Geometry by Donu Arapura

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About this book :-
Notes on Basic Algebraic Geometry written by Donu Arapura
This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for (future) experts in the field. The exposition serves a narrow set of goals, and necessarily takes a particular point of view on the subject.

Book Detail :-
Title: Notes on Basic Algebraic Geometry
Edition:
Author(s): Donu Arapura
Publisher:
Series:
Year: 2008
Pages: 41
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Classical Algebraic Geometry written by Igor Dolgachev cover the following topics.
Affine Geometry
Algebraic sets, Weak Nullstellensatz, Zariski topology, The Cayley-Hamilton theorem, Affine Varieties, Hilbert’s Nullstellensatz, Nilpotent matrices
Projective Geometry
Projective space, Projective varieties, Projective closure, Miscellaneous examples, Grassmanians, Elimination theory, Simultaneous eigenvectors
The category of varieties
Rational functions, Quasi-projective varieties, Graphs
Dimension theory
Dimension, Dimension of fibres, Simultaneous eigenvectors (continued)
Differential calculus
Tangent spaces, Singular points, Singularities of nilpotent matrices, Bertini-Sard theorem