### MATH 5320: Algebraic Geometry I

**Description:** This course is an introduction to algebraic varieties: affine and projective varieties, dimension of varieties and subvarieties, algebraic curves, singular points, divisors and line bundles, differentials, intersections.

**Prerequisites:** MATH 5211 and 5310, which may be taken concurrently.

**Credits:** 3

### MATH 5320 - Section 1: Algebraic Geometry I

**Description:** Algebraic geometry is a subject to use algebraic tools to understand geometry: dimension, smoothness, intersection, cohomology, and etc. At the same time, the geometric picture provides intuition to the study of algebraic objects. Algebraic geometry has become an indispensable tool for number theory and representation theory. In this course, we follow Gathmann's lecture notes on algebraic geometry (2003 version). We will cover topics of basic definitions of varieties, schemes, and sheaves. If time permits, we hope to introduce the cohomology theory for coherent sheaves and some basic intersection theory.

**Credits:** 3

**Sections: **Spring 2016 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

15290 | 5320 | 001 | Lecture | TuTh 02:00:00 PM-03:15:00 PM | MSB211 | Xiao, Liang |