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Ample line bundle
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Related lectures (15)
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Ample Invertible Sheaves
Introduces ample invertible sheaves and their properties in algebraic geometry.
Applications of Serre Duality
Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.
Serre Duality: General Case
Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.
Curve of Genus 2: Very Ample Divisors
Explores very ample divisors on curves of genus 2 and their implications.
Cartier Divisors and Invertible Sheaves
Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.
Redly Constructed Morphisms
Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.
Varieties with nef anti-canonical: Surjective Albanese
Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.
Canonical Divisors and Modular Forms
Covers canonical divisors on Riemann surfaces and properties of modular forms.
Albanese and Fourier Transform: Positive Characteristic
Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.
Modular Forms: Dimension Formula
Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.
Adjunctions and Applications
Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.
Finite Abelian Groups & Rings
Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.
Classification of Finite Abelian Groups
Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.
Euclidean Division: Uniqueness and Remainder
Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.
Integral Domains and Abelian Groups
Discusses integral domains, abelian groups, invertibility, zero divisors, prime elements, and group classification.
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