Mathematics 536 -- Introduction to Algebraic Geometry II-- Spring 2003

This course will begin with the algebraic geometry of schemes as an extension of the classical theory of algebraic varieties. The tools of cohomology and sheaf theory will be developed and applied to obtain invariants of classical algebraic geometric objects such as curves and surfaces. Applications in areas such as arithmetical algebraic geometry, toric varieties, commutative algebra and number theory will be discussed. The emphasis of the course will be on examples of schemes and general attributes of schemes as reflected in these examples. Topics will be drawn from the following :

  1. Sheaves
  2. Schemes and their properties
  3. Cohomology theory on schemes
  4. Curves
  5. Surfaces
  6. Toric varieties
  7. Schemes used in number theory

Prerequisites: Basics of linear algebra, rings, and fields. The standard graduate algebra course is sufficient. It will be useful to have some examples of varieties in mind to understand why schemes are useful

Text: Algebraic Geometry, by R. Hartshorne, Springer Graduate Texts in Mathematics 52 This text and additional references will be placed on reserve.

Course Format: There will be weekly homework assignments.

More Information: Contact J. Tunnell in Hill 546, email to tunnell@math or examine the course web site.