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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 
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
An introduction to derived algebraic geometry
This book contains below topics, Introduction and dgalgebras, Infinity categories and model categories, Consequences for dgalgebras, Simplicial structures, Geometric nstacks, Derived geometric nstacks.
Author(s): J. Eugster, J. P. Pridham
100 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
This note contains below topics, Preliminary Material, Lelong Numbers and Intersection Theory, Holomorphic Vector Bundles, Connections and Curvature, Bochner Technique and Vanishing Theorems, Numerically Eective Line Bundles, Seshadri Constants and the Fujita Conjecture, Algebraic Approach of the Fujita Conjecture, Regularization of Currents and Selfintersection Inequ alities, Use of MongeAmp ere Equations, Numerical Criteria for Very Ample Line Bundles, Holomorphic Morse Inequalities.
Author(s): Jean-Pierre Demailly
95 Pages