Projective Varieties: An Algebraic Study

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Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Projective Algebraic Sets: Definitions and Properties

Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.

Algebraic Varieties: Projective Sets and Topology

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Algebraic Varieties and Morphisms

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Algebraic Subsets of A^1

Covers algebraic subsets of A^1 and ideals with a finite set of points.

Albanese and Fourier Transform: Positive Characteristic

Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.