Course

MATH-328: Algebraic geometry I - Curves

Summary

Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory.

Lectures

Instructor

Aline Zanardini

Teaching & PhD Courses Advanced linear algebra I MATH-110(b) The purpose of this course is to introduce the basic notions of linear algebra and to prove the main results of the subject. Algebra V - Galois theory MATH-317 Galois theory lies at the interface of Field Theory and Group Theory. It aims to describe the algebraic symmetries of fields. We will focus on Galois theory for finite field extensions and some applications. Algebraic geometry I - Curves MATH-328

Official source

https://edu.epfl.ch/coursebook/en/algebraic-geometry-i-curves-MATH-328

Moodle Page

http://go.epfl.ch/MATH-328

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Summary

Lectures

Instructor

Aline Zanardini

Official source

https://edu.epfl.ch/coursebook/en/algebraic-geometry-i-curves-MATH-328

Moodle Page

http://go.epfl.ch/MATH-328

About this result

Lectures in this course (36)

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Lenstra's Algorithm: Integer Factorization

Covers Lenstra's Algorithm for integer factorization, which efficiently computes prime factors of an integer.

Algebraic Varieties in Linear Algebra

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

Variety Defined as the Closure of VCA

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

Complex Manifolds: GAGA Principle

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

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