Free online courseAlgebraic geometry

Course content

• Video class: What is...algebraic geometry?

  0h17m

• Exercise: What is the main focus of algebraic geometry?

• Video class: What are...algebraic varieties?

  0h14m

• Exercise: What is a fundamental concept in algebraic geometry?

• Video class: What are...conic sections?

  0h09m

• Exercise: What Determines the Type of a Conic Section?

• Video class: What are...ideals of sets?

  0h12m

• Exercise: What is a key concept in algebraic geometry?

• Video class: What is...Hilbert’s Nullstellensatz?

  0h10m

• Exercise: What is Hilbert's Nullstellensatz primarily concerned with?

• Video class: What is...the coordinate ring?

  0h12m

• Exercise: What is a coordinate ring in algebraic geometry?

• Video class: What is...the Zariski topology?

  0h10m

• Exercise: What is the Zariski topology primarily composed of in algebraic geometry?

• Video class: What is...the Zariski topology in algebra?

  0h10m

• Exercise: What is a key goal of algebraic geometry?

• Video class: What is...the dimension of a variety?

  0h10m

• Exercise: What is the correct notion of dimension in algebraic geometry?

• Video class: What are...regular functions?

  0h10m

• Exercise: What is a regular function in algebraic geometry?

• Video class: What is...the identity theorem?

  0h11m

• Exercise: What is the Identity Theorem in complex analysis about?

• Video class: What are...examples of regular functions?

  0h09m

• Exercise: What is the concept behind localization in algebraic geometry?

• Video class: What are...sheaves, take 1?

  0h13m

• Exercise: What is a major distinction between real and complex manifolds?

• Video class: What are...sheaves, take 2?

  0h10m

• Exercise: What is a sheaf in the context of algebraic geometry?

• Video class: What are...sheaves, take 3?

  0h09m

• Exercise: What is a locality condition in the concept of sheaves?

• Video class: What are...examples of sheaves?

  0h13m

• Exercise: What is a fundamental concept illustrated by the graph example?

• Video class: What are...ringed spaces?

  0h11m

• Exercise: What is a key concept in understanding varieties through ringed spaces?

• Video class: What is...the Why of ringed spaces?

  0h12m

• Exercise: What is the key role of ringed spaces in algebraic geometry?

• Video class: What are...prevarieties?

  0h11m

• Exercise: What is an affine variety in algebraic geometry?

• Video class: What are...(abstract) varieties?

  0h09m

• Exercise: What is a key condition that distinguishes manifolds from problematic spaces in topology?