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Notes on Geometry I

By: Lars Andersson

Description: This note covers the following topics: Linear Algebra, Differentiability, integration, Cotangent Space, Tangent and Cotangent bundles, Vector fields and 1 forms, Multilinear Algebra, Tensor fields, Flows and vectorfields, Metrics.

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A Gallery of Algebraic Surfaces ; Geometry

By: Bruce Hunt

Description: The notion of a surface is a very classical one in technology, art and the natural sciences. Just to name a few examples, the roof of a building, the body of a string instrument and the front of a wave are all, at least in idealized form, surfaces. In mathematics their use is very old and very well developed. A very special class of (mathematical) surfaces, given by particularly nice equations, are the algebraic surfaces, the topic of this lecture. With mode...

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Bezouts Theorem a Taste of Algebraic Geometry 1

By: Stephanie Fitchett

Description: 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.

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Algebraic Geometry

By: Alexei Skorobogatov

Description: This note contains the following subtopics: Basics of commutative algebra, Affine geometry, Projective geometry, Local geometry, Divisors.

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Topics in Algebraic Geometry II

By: Caucher Birkar

Description: This note covers the following topics: Cohomology, Relative duality, Properties of morphisms of schemes, Cohen-Macaulay schemes, Hilbert and Quotient schemes.

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Algebraic Geometry ; Main Volume

By: Andreas Gathmann

Description: 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.

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Topics in Algebraic Geometry I

By: Caucher Birkar

Description: This note covers the following topics: Cohomology, Relative duality, Properties of morphisms of schemes, Cohen-Macaulay schemes, Hilbert and Quotient schemes.

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Introduction to Algebraic Geometry, Part 1

By: R.C. Churchill

Description: It is hoped that this note will assist students in untangling the morass: they approach the subject from what could cynically be described as a rather narrow perspective, but they contain far more than the usual amount of detail and they include simple examples illustrating how algebraic geometers would work within this limited context.

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Bezouts Theorem a Taste of Algebraic Geometry 2

By: Stephanie Fitchett

Description: 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.

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Lectures on Differential Geometry II

By: Wulf Rossmann

Description: This note contains on the following subtopics of Differential Geometry, Manifolds, Connections and curvature, Calculus on manifolds and Special topics.

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Real Plane Algebraic Curves I

By: M.J. De La Puente

Description: This note explains the following topics: Affine and projective curves: algebraic aspects, Affine and projective curves: topological aspects.

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An Introduction to Complex Algebraic Geometry

By: Chris Peters

Description: 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.

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Abelian Varieties ; Geometry

By: J.S. Milne

Description: 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.

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Semi-riemann Geometry and General Relativity

By: Shlomo Sternberg

Description: This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms.

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The Geometry of K3 Surfaces

By: David R. Morrison

Description: This is a course note about K3 surfaces and several related topics.

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Lectures on Riemannian Geometry, Part II: Complex Manifolds

By: Stefan Vandoren

Description: This is an introductory lecture note on the geometry of complex manifolds. Topics discussed are: almost complex structures and complex structures on a Riemannian manifold, symplectic manifolds, Kahler manifolds and Calabi-Yau manifolds,hyperkahler geometries.

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A Course in Riemannian Geometry

By: David R. Wilkins

Description: From the table of contents: Smooth Manifolds; Tangent Spaces; Affine Connections on Smooth Manifolds; Riemannian Manifolds; Geometry of Surfaces in R3; Geodesics in Riemannian Manifolds; Complete Riemannian Manifolds; Jacobi Fields.

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Lectures on Fractals and Dimension Theory I

By: Mark Pollicott

Description: This note covers the following topics: Basic Properties and Examples, Iterated Function Schemes, Computing dimension, Some Number Theory and algorithms, Measures and Dimension, Classic results: Projections, Slices and translations, Tranversality and Iterated function schemes with overlaps.

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Lectures on Logarithmic Algebraic Geometry I

By: Arthur Ogus

Description: This book explains the following topics: The geometry of monoids, Log structures and charts, Morphisms of log schemes, Differentials and smoothness, De Rham and Betti cohomology.

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Riemannian Geometry Lecture Notes I

By: H.M. Khudaverdian

Description: This lecture note covers the following topics: Riemannian manifolds, Covariant differentiaion, Parallel transport and geodesics, Surfaces in E3 and Curvtature tensor.

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