Concept

Linear system of divisors

Related lectures (22)

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Algebraic Geometry: Regularity and Divisors

Explores regularity, divisors, prime divisors, and uniqueness in algebraic geometry.

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Canonical Divisors and Modular Forms

Covers canonical divisors on Riemann surfaces and properties of modular forms.

Modular Forms: Dimension Formula

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Curve of Genus 2: Very Ample Divisors

Explores very ample divisors on curves of genus 2 and their implications.

Regularity of Curves

Explores the regularity of curves over a field and the importance of specific properties for curve regularity.

Albanese and Fourier Transform: Positive Characteristic

Explores Albanese varieties, Fourier-Mukai transforms, and positive characteristic applications.

Divisors

Explains divisors, common divisors, and greatest common divisors with illustrative examples.

Linear Systems: Operations and Solutions

Explores linear systems, row operations, and solution methods, emphasizing geometric interpretations and unique solutions.

Finite Abelian Groups & Rings

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Integral Domains and Abelian Groups

Discusses integral domains, abelian groups, invertibility, zero divisors, prime elements, and group classification.

Least Squares Method Applications II

Explores data approximation with non-linear curves using the least squares method in 2D and 3D spaces.

Classification of Finite Abelian Groups

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.

Algebraic Multiplicity, Geometric Multiplicity

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

Incidence Geometry & Elliptic Curves

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Bézout's Theorem and Cayley-Bacharach

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.

Normal Equations in Square Geometry

Explores normal equations in square geometry, discussing properties and geometric relationships of normal lines in a square ABCD.

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Untitled