Coherent sheaves on the projective line

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The projective line is the simplest example of a non-affine variety and is a great place to have a first look at the notion of (quasi-)coherent sheaves. In this video, we give a hands-on definition of coherent sheaves on the projective line, by "gluing" together coherent sheaves on two affine patches along the intersection. We also define morphisms between them and see how it gives rise to an abelian category. We look in depth at the line bundles, which show the interesting feature that coherent sheaves can be the same on the affine patches but differ because they are glued together in different ways. We show how they are really different by computing the space of morphisms between them.
  1. DanielChanMaths
  2. Daniel Chan
  3. mathematics
  4. algebraic geometry
  5. sheaves
  6. projective line
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Комментарии
Автор

Great videos! I really like the geometric intuition spelled out.

toyeshjayaswal
Автор

Daniel, this is fantastic content. You're a great teacher and I think yt needs way more math at this level than it has right now. I think tons of math students will find this useful; thanks for posting!

BenSpitz