Lecture

Projective Varieties: An Algebraic Study

Related lectures (31)

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Projective Varieties: Invariants and Dimensions

Covers invariants and dimensions of projective varieties, emphasizing their importance.

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Compact Manifolds Classification

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Norm Extension in Finite Fields

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Automorphisms of Projective Varieties

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

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.