Math 545 Algebraic Curves & Riemann Surfaces Fall 2022

Timings

• Lecture: 10-11 MWF, location Wrighton 201

• Office hours: 9-10 W + 11-12 F, Cupples 204B

Resources

• The two main resources for the course are Fulton's Algebraic Curves (out of print, freely available here) and my notes for some sections of the course (available here).

• The course is also heavily influenced by the textbook Algebraic Curves & Riemann Surfaces by Rick Miranda.

• You might compare the notes from this course (more of a complex geometry emphasis), this course and this course.

We will cover some additional topics involving curves, likely including:

• Moduli of curves (notes, more notes, even more notes)

• Free resolutions & Green's conjecture (notes, notes, notes)

Here is the anthology of final papers submitted by students.

Assessment

• Participation - presenting 3 examples in class, contributing to discussion, attendance (30%)

• Homework - roughly every two weeks due at 11:59pm CT on Sundays (30%)

• Self-reflections - roughly every two weeks due at 11:59pm CT on Sundays (10%)

• Final or Paper - take-home exam from 8:00am CT 12/16 - 8:00am CT 12/17 or final paper on a topic inspired by the course due 11:59pm CT on 12/18. You should let me know your topic if writing a paper by 12/9 (30%)

Piazza bonus points: Each time you post a (mathematical!) question or answer on Piazza, you will receive 1 bonus point. These count as 1 point towards your overall homework score up to a maximum of 20 points. For example, if you dropped 15 points on homework throughout the semester and asked 5 questions on Piazza, your score for homework would be as if you only dropped 10 points. The deadline for Piazza points is 11:59pm the day before the final.

Attendance: You are permitted six unexplained absences without penalty. After that you will drop 1% for each missed class with a maximum of 10% deduction. If you have to miss a class email ahead explaining your absence and, if a legitimate conflict, no absence will be c0unted.

Dropped scores: I will drop the lowest homework score and allow for two missed self-reflections. Because of this and the Piazza bonus points I don't allow for makeups under any circumstances.

Resurrection final: We will use a resurrection final in this course. This means that we will calculate two grades: G1 = grade calculated as above, and G2 = grade calculated with homework counting 0% and final exam / paper counting 70%. Your final grade will be max(G1, G2).

Virtual testing: I will offer a virtual option for the final in circumstances such as quarantine due to sickness or potential exposure to covid-19.

Grading scale: I will use a 'European' grading scale throughout the course, where 70% is an A, 60% is a B+, 50% is a B, 40% is a C. There are no 'minus' grades in this course, and I will award an A+ for scores exceeding 90%. The consequence of this is that exams will require more creative thought and that you might not have time to answer all questions. A pass in the class is a C or higher, a high pass (if available) is 70% or higher.

Syllabus

This class may be helpful for billiards. Terms and conditions may apply.