Math 8254: Algebraic Geometry II

COURSE SYLLABUS

Spring 2018

CLASS MEETINGS: MW 3:35-4:50 (Vincent Hall 313)

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.math.umn.edu/~voronov/8254-18/ and NOT handed out in class.

OFFICE HOURS (tentative): Mon 2:30-3:20, Wed 1:25-2:15, Thu 11:15-12:05 or by appointment.

TEXT:  Algebraic Geometry, 1st edition, 1977, by Robin Hartshorne. Available for purchase at the bookstore and online. There is also a hard copy on reserve at the Math Library. Another useful book is Vakil's The Rising Sea, free on the web.

CONTENT: In the Fall, we built a lot of theoretical foundations of Algebraic Geometry, such as the functor of points for solutions of polynomial systems, affine schemes, inductive and projective limits, quasi-coherent and similar sheaves, exact functors and Čech H0, construction of schemes by gluing, affine and projective spaces. In the Spring Semester, I plan to involve more examples, covering the following topics: global schemes (Noetherian schemes, fibered products, Čech cohomology and cohomology as a derived functor), affine, étale and smooth morphisms, projective schemes, regular and smooth points, normalization, Kähler differentials, algebraic curves and the Riemann-Roch theorem. This roughly corresponds to Chapters 2, 3, and 4 of Hartshorne's textbook.

PREREQUISITE: Math 8353: Algebraic Geometry I. Some familiarity with Commutative and Homological Algebra will be helpful.

GETTING HELP:

REQUIREMENTS: : There will be homeworks due every other week, but no exams.

GRADING: Based on your homework. 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.

IMPORTANT DATES:

January 17: First class meeting.

January 29: First homework due.

March 5-9: I am in Philadelphia for a conference, no classes.

March 10-18: Spring Break.

May 4: Last class meeting.

Page created on 12/26/2017. Coverage changed on 01/17/2018. Important dates changed on 01/22/2018.