Lectures related to Projective variety

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

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

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

Introduces affine varieties and covers morphisms between them and their coordinate rings.

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

Explores the Albanese morphism of varieties with Kodaira dimension zero in positive characteristic.

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

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

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

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

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

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

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

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

Covers the study of projective varieties and their relation to compact manifolds.

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

Explores integration theory over real numbers and Berkovich spaces, revealing intriguing asymmetries and unsolved conjectures.

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Explores group actions on varieties, including orbits, stabilizers, and G-invariant morphisms.