MATH 561
Introduction to Algebraic Geometry 1.
Mathematics
College of Physical and Mathematical Sciences
Course Description
Basic definitions and theorems on affine, projective, and quasi-projective varieties.
When Taught
Fall Even Years
Grade Rule
Grade Rule 8: A, B, C, D, E, I (Standard grade rule)
Min
3
Fixed
3
Fixed
3
Fixed
0
Other Prerequisites
Math 571 or concurrent enrollment.
Title
Overview
Learning Outcome
Algebraic plane curves
Rational curves
Relation with field theory
Rational maps
Singular and nonsingular points
Projective spaces
Affine varieties
Affine space and the Zariski topology
Regular functions
Regular maps
The Zariski topology on projective space
Products and maps of quasi-projective space
Properness of projective maps
Dimension.
Title
Learning Outcomes
Learning Outcome
Students should achieve mastery of the topics listed in the minimal learning outcomes on the Math 561 Wiki page. This means they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor.
