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Lecture
Applications of Serre Duality
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Serre Duality: General Case
Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Varieties with nef anti-canonical: Surjective Albanese
Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.
Projective Morphisms: Theory and Applications
Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.
Albanese and Fourier Transform: Positive Characteristic
Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.
Curve of Genus 2: Very Ample Divisors
Explores very ample divisors on curves of genus 2 and their implications.
Curves with Poritsky Property and Liouville Nets
Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.
Curves in Space: Parametric Equations and Surfaces
Covers the equations for curves and surfaces in space, including parametric and particular surfaces.
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.
Projective Geometry: Tangent Lines
Discusses the correction of tangent lines and projective plane curves, exploring topological applications and curve structure.
