Algebraic Geometry: Forms and Maps

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Related lectures (31)

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Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Meromorphic Functions & Differentials

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

Harmonic Forms: Main Theorem

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

Riemann Zeta Function

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

Regularity and Geometric Meaning

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

Varieties with nef anti-canonical: Surjective Albanese

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

Tangent Spaces in Algebraic Geometry

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.