Algebraic Geometry a start up course

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

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

Abelian Varieties

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

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

Algebraic Geometry pdf

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

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

Riemann Surfaces and Algebraic Curves

This note describes the relation between algebraic curves and Riemann surfaces.

Author(s): Joel W. Robbin

8 Pages

A Stab at some Algebraic Geometry

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Author(s): NA

NA Pages

Introduction to projective varieties

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NA Pages

Introduction to Numerical Algebraic Geometry

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NA Pages

Introduction to Algebraic Geometry

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NA Pages