Lectures related to Projective Varieties: Invariants and Dimensions

Topology of Riemann Surfaces

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

Varieties with nef anti-canonical: Surjective Albanese

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

Albanese Morphism: Kodaira Dimension Zero

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

Complex Manifolds: GAGA Principle Log in to Mediaspace to watch this video

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

Adjunctions and Applications Log in to Mediaspace to watch this video

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

Automorphisms of Projective Varieties Log in to Mediaspace to watch this video

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

Modern Algebraic Geometry Log in to Mediaspace to watch this video

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

Projective Varieties: An Algebraic Study Log in to Mediaspace to watch this video

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

Algebraic Varieties and Morphisms Log in to Mediaspace to watch this video

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

Regularity and Geometric Meaning Log in to Mediaspace to watch this video

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

G-modules and G-varieties Log in to Mediaspace to watch this video

Explores the embedding of chi-varieties into vector spaces with linear actions.

Algebraic Varieties: Projective Sets and Topology Log in to Mediaspace to watch this video

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

Dimension of Algebraic Variety Log in to Mediaspace to watch this video

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Projective Algebraic Sets: Definitions and Properties Log in to Mediaspace to watch this video

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

The Regular Representation Log in to Mediaspace to watch this video

Introduces the regular representation, a key tool for studying group actions on varieties.

Smooth Projective Varieties Log in to Mediaspace to watch this video

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

Affine Varieties Log in to Mediaspace to watch this video

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

Projective Morphisms: Theory and Applications Log in to Mediaspace to watch this video

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

Field of Rational Functions Log in to Mediaspace to watch this video

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.

Compact Manifolds Classification Log in to Mediaspace to watch this video

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