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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 
Introduction to Algebraic Geometry by JustinR.Smith
This note covers classical result, Affine varieties, Local properties of affine varieties, Varieties and Schemes, Projective varieties and Curves.
Author(s): JustinR.Smith
663 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
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
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
Topics in Classical Algebraic Geometry
This book explains the following topics: Polarity, Conics, Plane cubics, Determinantal equations, Theta characteristics, Plane Quartics, Planar Cremona transformations, Del Pezzo surfaces, Cubic surfaces, Geometry of Lines.
Author(s): Igor V. Dolgachev
524 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
Foundations of Differential Geometry (ps file)
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Author(s): NA
NA Pages
Yuriy Drozd Intriduction to Algebraic Geometry
This note explains the following topics: Affine Varieties, Hilbert’s Nullstell, Projective and Abstract Varieties, Grassmann varieties and vector bundles, Finite morphisms, Dimension Theory, Regular and singular points, Tangent space, Complete local rings, Intersection theory.
Author(s): Yuriy Drozd
104 Pages
Complex algebraic surfaces class
This note explains the theory of (complex) algebraic surfaces, with the goal of understanding Enriques' classification of surfaces.
Author(s): Ravi Vakil
NA Pages
This note explains the following topics: Affine and projective curves: algebraic aspects, Affine and projective curves: topological aspects.
Author(s): M.J. de la Puente
25 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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Introduction to projective varieties
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Numerical curves and their applications to algebraic curves
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Topics In Algebra Elementary Algebraic Geometry
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Algebraic geometry and projective differential geometry
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