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Seven Lectures on the Universal Algebraic Geometry
This note contains below topics, What is the Universal Algebraic Geometry Lecture, Algebraic sets and algebraic varieties Lecture, Geometric properties and geometric relations of algebras Lecture, Algebraic geometry in groupbased algebras Lecture, Isomorphisms of categories of algebraic sets Lecture, Algebraic geometry in the First Order Logic FOL Lecture, Generic view, Some information from universal algebra, Algebras with a fixed algebra of constants, Systems of equations and algebraic sets, Lattices of algebraic sets, Categories of algebraic sets.
Author(s): Boris Plotkin
87 Pages 
Lectures notes in universal algebraic geometry
This note contains below topics, Algebraic structures, Subalgebras direct products homomorphisms, Simplifications of terms, 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.
Author(s): A. Shevlyakov
67 Pages
Lecture Notes on Quiver Representations and Moduli Problems in Algebraic Geometry
This note contains below topics, Moduli problems and moduli functors, The Beilinson spectral sequence, Algebraic group actions and quotients, Geometric invariant theory, Moduli spaces of quiver representations, Framed representations, Double quivers and Hamiltonian reduction, Nakajima quiver varieties.
Author(s): Alexander Soibelman
82 Pages
Lecture Notes on Multi loop Integral Reduction and Applied Algebraic Geometry
These notes are for lectures on integral reduction and applied algebraic geometry techniques, given at a school on amplitudes in Beijing in 2016. They show how algebraic geometry is used to reduce multiloop integrals.
Author(s): Yang Zhang
92 Pages
Seven Lectures on the Universal Algebraic Geometry
This note contains below topics, What is the Universal Algebraic Geometry Lecture, Algebraic sets and algebraic varieties Lecture, Geometric properties and geometric relations of algebras Lecture, Algebraic geometry in groupbased algebras Lecture, Isomorphisms of categories of algebraic sets Lecture, Algebraic geometry in the First Order Logic FOL Lecture, Generic view, Some information from universal algebra, Algebras with a fixed algebra of constants, Systems of equations and algebraic sets, Lattices of algebraic sets, Categories of algebraic sets.
Author(s): Boris Plotkin
87 Pages
Notes on derived algebraic geometry
This note contains below topics, Overview Higher algebra, Derived commutative algebra, Derived algebraic geometry, The stack of perfect modules.
Author(s): Can Yaylali
63 Pages
This note contains below topics, Examples of homogeneous varieties, Auxilliary varieties, Topology and consequences, Projective dierential invariants, Varieties with degenerate Gauss images, When can a uniruled variety be smooth, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, Systems of quadrics with tangential defects, Recognizing uniruled varieties.
Author(s): Joseph M. Landsberg
70 Pages
Introduction to Algebraic Geometry by JustinRSmith
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
Computational Algebraic Geometry by Wolfram Decker
This PDF book covers the following topics related to Algebraic Geometry, General Remarks on Computer Algebra Systems, The GeometryAlgebra Dictionary, Affine Algebraic Geometry, Ideals in Polynomial Rings, Affine Algebraic Sets, Hilberts Nullstellensatz, Irreducible Algebraic Sets, Removing Algebraic Sets, Polynomial Maps, The Geometry of Elimination, Noether Normalization and Dimension, Local Studies, Projective Algebraic Geometry, The Projective Space, Projective Algebraic Sets, Affine Charts and the Projective Closure, The Hilbert Polynomial, Computing, Standard Bases and Singular, Applications, Ideal Membership, Elimination, Radical Membership, Ideal Intersections, Ideal Quotients, Kernel of a Ring Map, Integrality Criterion, Noether Normalization, Subalgebra Membership, Homogenization, Dimension and the Hilbert Function, Primary Decomposition and Radicals, Buchbergers Algorithm and Field Extensions, Sudoku, A Problem in Group Theory Solved by Computer Algebra, Finite Groups and Thompsons Theorem, Characterization of Finite Solvable Groups.
Author(s): Wolfram Decker, Gerhard Pfister
133 Pages