Lectures related to Regularity and Geometric Meaning

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

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.

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

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

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

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

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Explains the independence of events and sets in an algebraic context.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

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

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

Explores geometric examples related to linear applications in algebra.

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

Covers the concept of locally Noetherian schemes in algebraic geometry.

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.

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

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.