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Foundations Of Algebraic Geometry
This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for experts in the field. Topics covered includes: Sheaves, Schemes, Morphisms of schemes, Useful classes of morphisms of schemes, Closed embeddings and related notions, Fibered products of schemes, and base change, Geometric properties: Dimension and smoothness, Quasicoherent sheaves, Quasicoherent sheaves on projective A-schemes, Differentials,Derived functors, Power series and the Theorem on Formal Functions, Proof of Serre duality.
Author(s): Ravi Vakil
764 Pages 
Introduction to Algebraic Geometry by Emilia Mezzetti
This note covers introduction, Affine and projective space, Algebraic sets, Examples of algebraic sets, The ideal of an algebraic set and the Hilbert Nullstellensatz, The projective closure of an affine algebraic set, Irreducible components, Dimension, Regular and rational functions, Regular and rational maps, Products of quasi projective varieties, The dimension of an intersection, Complete varieties and the tangent space.
Author(s): Emilia Mezzetti
66 Pages
Foundations Of Algebraic Geometry
This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for experts in the field. Topics covered includes: Sheaves, Schemes, Morphisms of schemes, Useful classes of morphisms of schemes, Closed embeddings and related notions, Fibered products of schemes, and base change, Geometric properties: Dimension and smoothness, Quasicoherent sheaves, Quasicoherent sheaves on projective A-schemes, Differentials,Derived functors, Power series and the Theorem on Formal Functions, Proof of Serre duality.
Author(s): Ravi Vakil
764 Pages
Algebraic Geometry Lecture Notes
This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Covered topics are: Basics of category theory, Sheaves, Abelian sheaves, Schemes, Morphisms of schemes, Sheaves of modules, More properties of morphisms, Projective morphisms, Projective morphisms, Flat morphisms and descent, Differentials Divisors, Divisors on curves, Homological algebra, Sheaf cohomology, Cohomology of quasicoherent sheaves, Cohomology of projective spaces, Hilbert polynomials, GAGA, Serre duality for projective space, Dualizing sheaves and RiemannRoch, CohenMacaulay schemes and Serre duality, Higher RiemannRoch and Etale cohomology.
Author(s): Prof. Kiran Kedlaya
NA Pages
Bezouts Theorem A taste of algebraic geometry
This note covers the following topics: The Pre-cursor of Bezout’s Theorem: High School Algebra, The Projective Plane and Homogenization, Bezout’s Theorem and Some Examples.
Author(s): Stephanie Fitchett, Florida Atlantic University Honors College
11 Pages
These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory.
Author(s): J.S. Milne
NA Pages
An Introduction to complex algebraic geometry
The material presented here consists of a more or less self contained advanced course in complex algebraic geometry presupposing only some familiarity with the theory of algebraic curves or Riemann surfaces. But the goal, is to understand the Enriques classification of surfaces from the point of view of Mori theory.
Author(s): Chris Peters
129 Pages
Notes on basic algebraic geometry
This is an introductory course note in algebraic geometry. Author has trodden lightly through the theory and concentrated more on examples.Covered topics are: Affine Geometry, Projective Geometry, The category of varieties, Dimension theory and Differential calculus.
Author(s): Donu Arapura
41 Pages
Riemann Surfaces and Algebraic Curves
This note describes the relation between algebraic curves and Riemann surfaces.
Author(s): Joel W. Robbin
8 Pages
Introduction to Algebraic Geometry
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NA Pages
A Stab at some Algebraic Geometry
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Introduction to projective varieties
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Algebraic Geometry a start up course
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NOTES ON ALGEBRAIC GEOMETRIC CODES Introduction
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Introduction to Algebraic Geometry
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