Lecture

Modern Algebraic Geometry: Schemes and Affine Schemes

Related lectures (31)

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

Projective Algebraic Sets: Definitions and Properties

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

Projective Morphisms: Theory and Applications

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

Varieties with nef anti-canonical: Surjective Albanese

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

Variety Defined as the Closure of VCA

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

Topology of Riemann Surfaces

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

Morphisms and Local Rings

Explores morphisms, regularity, varieties, local rings, and evaluation morphism in algebraic geometry.

Affine Varieties and Hypersurfaces

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

Affine Algebraic Sets

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

Homogeneous Ideals and Regular Rings

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Regularity and Integrality

Covers regularity and integrality in local Noether rings and affine rings.

Affine Varieties

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

Regularity and Geometric Meaning

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

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Locally Noetherian Schemes

Covers the concept of locally Noetherian schemes in algebraic geometry.

Adjunctions and Applications

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

Riemann Zeta Function

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Weil Conjectures: Rationality and Function Equation

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