Algebraic Varieties: Projective Sets and Topology

Related lectures (31)

Page 3 of 4

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

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

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

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

Introduces projective space and algebraic sets, discussing homogeneous coordinates, ideals, and generators.

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

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

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

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Covers the concept of algebraic quotients in the context of a-variety.