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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
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
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
Notes on basic algebraic geometry
This is an introductory course note in algebraic geometry. The author has trodden lightly through the theory and concentrated more on examples.
Author(s): Donu Arapura
41 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
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
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
Foundations of Differential Geometry (ps file)
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Author(s): NA
NA 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
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
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Author(s): NA
NA Pages
Algebraic Geometry a start up course
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Author(s): NA
NA Pages
Numerical curves and their applications to algebraic curves
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Author(s): NA
NA Pages
NOTES ON ALGEBRAIC GEOMETRIC CODES Introduction
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Author(s): NA
NA Pages
