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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 
Lecture Notes for Algebraic geometry
This note covers notation, What is algebraic geometry, Affine algebraic varieties, Projective algebraic varieties, Sheaves, ringed spaces and affine algebraic varieties, Algebraic varieties, Morphisms, Products, Dimension, The fibres of a morphism, Sheaves of modules, Hilbert polynomials and bezouts theorem, Schemes, Products of preschemes, Relative differentials, Cartier divisors, Rational equivalence and the chow group, Proper push forward and flat pull back, Chern classes of line bundles and chern classes of vector bundles.
Author(s): Leonardo Constantin Mihalcea
132 Pages
Undergraduate Algebraic Geometry
This note covers Playing with plane curves, Plane conics, Cubics and the group law, The category of affine varieties, Affine varieties and the Nullstellensatz, Functions on varieties, Projective and biration algeometry, Tangent space and non singularity and dimension.
Author(s): Miles Reid, University of Warwick
134 Pages
Algebraic Geometry I Lecture Notes Roman Bezrukavnikov
The contents of this book include: Course Introduction, Zariski topology, Affine Varieties, Projective Varieties, Noether Normalization, Grassmannians, Finite and Affine Morphisms, More on Finite Morphisms and Irreducible Varieties, Function Field, Dominant Maps, Product of Varieties, Separateness, Sheaf Functors and Quasi-coherent Sheaves, Quasi-coherent and Coherent Sheaves, Invertible Sheaves, (Quasi)coherent sheaves on Projective Spaces, Divisors and the Picard Group, Bezout’s Theorem, Abel-Jacobi Map, Elliptic Curves, KSmoothness, Canonical Bundles, the Adjunction Formulaahler Differentials, Cotangent Bundles of Grassmannians, Bertini’s Theorem, Coherent Sheves on Curves, Derived Functors, Existence of Sheaf Cohomology, Birkhoff-Grothendieck, Riemann-Roch, Serre Duality, Proof of Serre Duality.
Author(s): Roman Bezrukavnikov
63 Pages
Lectures notes in universal algebraic geometry Artem N. Shevlyakov
The contents of this book include: Introduction, Algebraic structures, Subalgebras, direct products, homomorphisms, Equations and solutions, Algebraic sets and radicals, Equationally Noetherian algebras, Coordinate algebras, Main problems of universal algebraic geometry, Properties of coordinate algebras, Coordinate algebras of irreducible algebraic sets, When all algebraic sets are irreducible, The intervention of model theory, Geometrical equivalence, Unifying theorems, Appearances of constants, Coordinate algebras with constants, Equational domains, Types of equational compactness, Advances of algebraic geometry and further reading.
Author(s): Artem N. Shevlyakov
67 Pages
Basic Modern Algebraic Geometry
This note covers the following topics: Functors, Isomorphic and equivalent categories, Representable functors, Some constructions in the light of representable functors, Schemes: Definition and basic properties, Properties of morphisms of schemes, general techniques and constructions.
Author(s): Audun Holme
111 Pages
An introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture. Warning: These notes are less polished than the others.
Author(s): J.S.Milne
172 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
This book explains the following topics: What is algebraic geometry, Functions, morphisms, and varieties, Projective varieties, Dimension, Schemes, Morphisms and locally ringed spaces, Schemes and prevarieties, Projective schemes, First applications of scheme theory, Hilbert polynomials.
Author(s): Andreas Gathmann
214 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
A Gallery of Algebraic Surfaces
This note explains the following topics: Algebraic surfaces, Singularities, Maximal numbers of singularities, Quartics, Enumerative geometry.
Author(s): Bruce Hunt
25 Pages
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A Stab at some Algebraic Geometry
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Algebraic Geometry a start up course
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Introduction to Algebraic Geometry
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Topics In Algebra Elementary Algebraic Geometry
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