Lectures notes in universal algebraic geometry Artem N. Shevlyakov
Lectures notes in universal algebraic geometry Artem N. Shevlyakov
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.
This note covers the following
topics: Functors, Isomorphic and equivalent categories, Representable functors,
Some constructions in the light of representable functors, Schemes: Definition
and basic properties, Properties of morphisms of schemes, general techniques and
constructions.
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
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.
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.
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.