MAT 402 (Introduction to Algebraic Geometry for Undergraduates) - Spring 2021

Time and Place : TuTh 1:15- 2:35; Zoom Meeting

Instructor : Radu Laza

Email :  radu.laza@stonybrook.edu

Office Hours: Thr 2:30-4 (same link as the class), Tue 11-12:30

Overview

This is an introductory course in Algebraic Geometry for undergraduates. The target audience are students aiming for graduate school, or just wanting to learn something beyond the standard undergraduate material. This is an undergraduate seminar class, meaning that it will be a mixture of lectures on basic material, free discussion, and presentations by the participants.
I aim to be both self-contain, and ambitious in the material covered. This means that there are few formal requirements to attend (though some abstract algebra, and basic topology are recommended). On the other hand, some commitment (e.g. regular participation) and effort on your side are necessary.

Textbook

Announcements

Grading&Policy


Schedule

WeekTopicReferences
(1) Feb 4 What is algebraic geometry?
(Overview and some examples)
(2) Feb 9, 11 Overview
Projective Space
(3) Feb 16, 18 Projective space (coordinates, Why CP^n?)
(4) Feb 23, 25 Degree, Linear Transformations, Bezout Theorem
(5) Mar 2, 4 Conics (Normal form, Parameterization) [Reid] I.1
(6) Mar 9, 11 Cubics [Reid] I.2
(7) Mar 16, 18 Affine varieties, Nullstellensatz [Reid] II.3
(8) Mar 23, 25 The coordinate ring [Reid] II.4
(9) Mar 30, Apr 1 Smoothness, Dimension [Reid] III.6
(10) Apr 6, 8 Blow-up, Birational Equivalances, Cremona transformation [Reid] III.5
(11) Mar 30, Apr 1 Cubic surfaces [Reid] III.7
(12) Apr 20, 22 Presentations & Discussion (1)
(13) Apr 27, 29 Presentations & Discussion (2)
(14) May 4, 6 Presentations & Discussion (3)