Lectures related to Complex Manifolds: GAGA Principle

Projective Varieties: An Algebraic Study

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

Topology of Riemann Surfaces

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

Variety Defined as the Closure of VCA

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

Projective Varieties: Invariants and Dimensions

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

Adjunctions and Applications

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

Riemann Surfaces: Complex Manifolds

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Conformal Blocks: Functions on Moduli Spaces

Covers conformal blocks and their significance in complex structures and moduli spaces.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Regularity and Geometric Meaning

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

Algebraic Varieties and Morphisms

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

Automorphisms of Projective Varieties

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

Compact Manifolds Classification

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

Varieties with nef anti-canonical: Surjective Albanese

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

Modern Algebraic Geometry

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

Algebraic Varieties in Linear Algebra

Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.

Albanese Morphism: Kodaira Dimension Zero

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Projective Algebraic Sets: Definitions and Properties

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

Morphisms and Local Rings

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