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Morphism of algebraic varieties
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Morphisms and Local Rings
Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.
Morphisms between Affine Varieties
Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.
Fixed points, orbits, and stabilizers
Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.
Algebraic Functions: Two Gendarmes
Explores algebraic functions, limits, and behavior as x approaches infinity.
Remarks about the Quotient
Explores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.
Adjunctions and Applications
Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.
Algebraic Varieties in Linear Algebra
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Ring Theory: Morphisms and Isomorphisms
Covers commutative ring morphisms, subrings, and injective ring morphisms.
Affine Algebraic Varieties: Zariski Topology
Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.
Ringed Spaces: Definitions and Properties
Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.