INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: (612) 624-0355
E-MAIL ADDRESS: voronov@umn.edu. You are welcome to use e-mail to send questions to me.
INTERNET: All class announcements and assignments will be posted on the class homepage http://www-users.cse.umn.edu/~voronov/8253f22/ and NOT handed out in class.
OFFICE HOURS (tentative): Mon 1:25-2:15 (in VinH 324 and on Zoom), Tue 12:20-1:10 (on Zoom), Thu 1:25-2:15 (on Zoom), or by appointment. Here is the Zoom link for office hours:
https://umn.zoom.us/j/96063441796?pwd=dnN0TC9Dc3NmRFVTS0l5Nk1VZlBSZz09
TEXTS: Algebraic Geometry, latest online edition, 2022, by Andreas Gathmann (only available online for free).
The Rising Sea, latest online edition, 2022, by Ravi Vakil (only available online for free).
Algebraic Geometry, 1st edition, 1977, by Robin Hartshorne is not required but might be a good alternative.
CONTENT: In the Fall semester, we will cover the following topics: affine and projective varieties, curves, surfaces, Grassmannians, rational and birational maps, blowing up, Zariski topology, schemes, quasi-coherent sheaves, differentials, smoothness, Čech cohomology. I plan to follow Gathmann's online notes pretty closely. The material on schemes is covered by Parts I, II, III and Chapters 19, 22, and 23 of Vakil's textbook. In Hartshorne's textbook, this semester's material roughly corresponds to Chapters I, II and Section III.4.
PREREQUISITES: Math 8201-02: General Algebra or equivalent. In reality, all you need is to be familiar with groups, rings, modules, and fields, as well as some basic topology (closed and open sets, connectedness, compactness, Hausdorffness, etc.)
GETTING HELP:
GRADING: Based on your homework, which will be due every other week. Please submit homework by uploading it in the pdf, jpg, or similar format to the course Gradescope page here. No exams. Class participation may be taken into account. Grades will be assigned on a curve. I expect you to put enough hard work to earn grades not lower than a B. The curve does not exclude the possibility of everybody getting A's, though, but this happens rather rarely.
COVID-19: :
IMPORTANT DATES:
September 7: First class meeting.
September 12-16: No class meetings (I will be at a conference in Prague). Work on the homework.
September 19: First homework due.
November 24-25: Thanksgiving Break.
December 14: Last class meeting.
Page created on 09/08/2022; Homework uploading link added on 09/20/22.