## MATHEMATICS 514 M1, COMPLEX ALGEBRAIC GEOMETRY II, FALL 2018

Instructor: Sheldon Katz
Phone/email: 265-6258, katzs AT illinois.edu
Office and Hours: 301 Altgeld Hall, Mondays 1-1:50, Thursdays 10-10:50, or by appointment
Class Time and location: TR 11-12:20, 447 Altgeld Hall
Text: C. Voisin, Hodge Theory and Complex Algebraic Geometry, I

Course Syllabus is here

Homework:
• Homework 1, due Tuesday, September 11
• Homework 2, due Tuesday, September 25.
• Homework 3, due Tuesday, October 9.
• Homework 4, due Tuesday, October 30.
• Homework 5, due Thursday, November 15. The posted (final) version replaces the preliminary version which was posted previously.
• Homework 6, due Tuesday, December 11.
• Clarifications
• In problem 1(a), assume that ρ is an algebraic homomorphism rather than merely a continuous homomorphism. This means that ρ(z) is a (matrix-valued) polynomial in z and its complex conjugate.
• There is a typo: what is written as ρ(z*)=(ρ(z))* should simply be ρ(z)=(ρ(z))*. Here I have been lazy implementing html and have appended a * to denote complex conjugation. The typo occurs once in problem 1(a) and then again right before stating 1(b).
• The point of problem 2 is to derive the Hodge decomposition for curves using only elementary techniques, so it's best not to use Hodge theory in the solution.

Homework solutions:
Notes:
• Office hours on Monday, Dec 10 are cancelled and rescheduled to 2pm on Friday, Dec 7. This will be my last office hour of the semester, but I will remain available by appointment.

Books on Reserve:
• Hodge Theory and Complex Algebraic Geometry, I, C. Voisin
• Principles of Algebraic Geometry, P. Griffiths and J. Harris, available in Math Library, Grainger Engineering Library, and as an e-book.
• Introduction to smooth manifolds, J. Lee, Graduate texts in mathematics 218, Springer, available in electronic and hardcopy formats.
• Several complex variables, Grauert and Fritzsche, Graduate texts in mathematics 1976, Springer, available in electronic and hardcopy formats.

Seminars and other activities of interest
• Here is some information for students thinking about working with me as a thesis advisor
• Graduate Student Algebraic Geometry Seminar, Wednesdays at 4, 2 Illini Hall
• Algebraic Geometry Seminar, Tuesdays at 3pm, 243 Altgeld Hall.
• Algebraic Geometry lunch, 12:30 Tuesdays, 403 Illini Union (except October 23, when it will be in 277 IU). This is an informal brown bag lunch, which will usually include informal 20 minute presentations designed to be friendly to grad students. If you would like to be on the mailing list for the seminar and the lunch, please request membership at this link.