MATH 214A : Algebraic Geometry
- Course description: This
is the first of a two-quarter introduction to algebraic geometry.
Affine, projective, and more general varieties, as a special class
of schemes. Complex algebraic varieties and relations to topology
and complex analysis.
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.
Instructor: Burt Totaro.
E-mail: totaro@math.ucla.edu.
Lecture: MWF 10-10:50,
MS 5148.
Office Hour: To be determined.
Textbook: Hartshorne's
Algebraic Geometry (Springer)
is the main book for the class. The UCLA Store should be selling it in their textbook department on floor A.
Roughly, I will cover Chapter I and sections
1-5 of Chapter II. Other useful
books include Kempf's Algebraic Varieties (Cambridge),
a short book that gets surprisingly far,
and Vakil's The Rising
Sea, free on the web.
Complex algebraic geometry (using differential geometry
and complex analysis) is not the main
focus of the class, but it is an important alternative point
of view. The essential reference
on complex algebraic geometry
is Griffiths and Harris's Principles of Algebraic Geometry (Wiley);
Huybrechts's Complex Geometry (Springer) is a shorter introduction.
Prerequisite: Math 215A
Commutative Algebra is required.
Grading: Based on three homework sets.
Course web page: http://www.math.ucla.edu/~totaro/214a.1.16w/index.html
Homework 1 (due January 20, 2016).
Homework 2 (due February 17, 2016).
Homework 3 (due March 7, 2016).