MATH 214A - Introduction to Algebraic Geometry - Winter 2017

Instructor

Martin Gallauer
Office hours: I am not going to hold fixed office hours. If you would like to chat, please let me know, and I'll be happy to meet.

Course description

This is the first of a two-quarter introduction to algebraic geometry. The second part will be taught by Professor Totaro in the Spring Quarter.

Topics include: affine, projective, and more general varieties, as a special class of schemes. Irreducibility, connectedness, products. Regular functions, rational functions, local rings. Tangent spaces, smoothness. Affine morphisms, proper morphisms, finite morphisms. Curves. Sheaf theory: coherent and quasi-coherent sheaves.

Prerequisite

Math 215A (Commutative Algebra) is required.

Location and time

Class: MWF 12-12:50 pm, MS 5117

Textbook

  • Hartshorne's Algebraic Geometry (Springer) is the main book for the class. Roughly, I will cover Chapter I and sections 1-5 of Chapter II.
  • Two other excellent textbooks are Vakil's The Rising Sea and Görtz-Wedhorn's Algebraic Geometry I.
  • The main reference for algebraic geometry is (still) EGA (Grothendieck et al.: Éléments de géométrie algébrique). Another increasingly popular option is the stacks project.

Homework and grading

This material is very dense and can't be absorbed without solving problems. Homework is therefore an integral part of the course. Your grade will be based on it as well.

Assignments: