Math 8254: Algebraic Geometry

COURSE SYLLABUS

Spring 2023

CLASS MEETINGS: M 1:55-2:25 in Vincent Hall 311 and WF 2:00-3:00 in Amundson Hall 116; Zoom link for class meetings, should you get sick or need to quarantine: Zoom here

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/8254s23/ and NOT handed out in class.

OFFICE HOURS (tentative): Office Hours (tentative): Mon 12:50-1:40 (in VinH 324 and on Zoom), Tue 12:20-1:10 (on Zoom), Fri 12:50-1:40 (in VinH 324 and on Zoom), or by appointment. Here is the Zoom link for office hours: Zoom here

TEXTS: Algebraic Geometry 2021/22 and 2002/03, latest online editions, 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 Spring semester, we will cover the following topics: coherent and quasi-coherent sheaves, differentials, Čech cohomology, projective schemes and Proj R, the Hilbert polynomial, Bézout's theorem, divisors, line bundles, very ample line bundles, Riemann-Hurwitz and Riemann-Roch for curves, intersection theory, and Chern classes, time permitting. I plan to follow Gathmann's online notes pretty closely. In Hartshorne's textbook, this semester's material roughly corresponds to the remaining part of Chapter II and parts of Chapters III and IV.

PREREQUISITES: Math 8253: Algebraic Geometry I or equivalent: affine and projective varieties, schemes.

GETTING HELP:

Work in study groups and learn from each other. See also How to Form a Successful Study Group.
Attend my office hours (see above).
E-mail: Send questions to me at voronov@umn.edu
Call me up at (612) 624-0355.

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 by midnight on the due date. No exams. Class participation will 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: :

Teaching mode: In person, in class. I will switch to Zoom in one way or another, if need be. If you can't attend a class meeting in person due to illness or quarantine, join the lecture via Zoom Meeting from your umn.edu Zoom account:
Join Zoom Lecture
https://umn.zoom.us/j/92246209888?pwd=Y3I0d2FrMTM2aHdGdWJGcmU4eFc1QT09
Meeting ID: 922 4620 9888
Passcode: uf9vSg
Masks: I will not be wearing a face mask in class, but will be putting one on when talking to you informally at a closer distance. I encourage you to wear masks, because the pandemic is not completely over and it is hard for you to keep social distance in class. However, the choice of wearing a mask is entirely up to you.
More details on symptoms and vaccinations: Advice and requirements on COVID-19 symptoms and prevention (pages 3-4).

IMPORTANT DATES:

January 18: First class meeting.

February 1: First homework due.

March 4-12: Spring Break.

April 17- May 1: Class meetings and office hours switch to Zoom, as I will be at a program on SuperGeometry and SuperModuli at the Simons Center for Geometry and Physics in Stony Brook.

May 1: Last class meeting.

Page created on 01/19/2023.