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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
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 I (PDF 20P)
This note contains the following subtopics of Algebraic Geometry, Theory of Equations, Analytic Geometry, Affine Varieties and Hilbert’s Nullstellensatz , Projective Varieties and Bezout’s Theorem, Epilogue
Author(s): Sudhir R. Ghorpade
20 Pages
Notes of an introductory course to Algebraic Geometry
This note covers the following topics: The correspondence between ideals and algebraic sets, Projections, Sheaves, Morphisms of Sheaves, Glueing Sheaves, More on Spec(R), Proj(R)is a scheme, Properties of schemes, Sheaves of modules, Schemes over a field, sheaf of differentials and Picard group.
Author(s): Sandra Di Rocco
NA 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
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
Algebraic Geometry, book in progress
This book covers the following topics: Elementary Algebraic Geometry, Dimension, Local Theory, Projective Geometry, Affine Schemes and Schemes in General, Tangent and Normal Bundles, Cohomology, Proper Schemes and Morphisms, Sheaves and Ringed Spaces.
Author(s): Jean Gallier
546 Pages
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NA Pages
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NA Pages
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A Stab at some Algebraic Geometry
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NA Pages
Introduction to Algebraic Geometry
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Topics In Algebra Elementary Algebraic Geometry
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Introduction to Algebraic Geometry
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