Algebraic Geometry
3
In person
Tuesdays, Thursdays 11am-12:20pm
Wachman 527
Wachman 530
Wednesdays 1-3pm, Thursdays 2-3pm and by appointment
W. Fulton, Algebraic Curves: an introduction to algebraic geometry
R. Hartshorne, Algebraic Geometry, Springer, 1977
I.R. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, 1977
Homework: 80%. Presentation: 20%.
Math 8011, 8012, 9014 or permission of instructor
To master basic concepts of algebraic geometry
This is a one-semester course on algebraic geometry. The goal is to learn affine and projective varieties, morphisms of varieties, function fields and rational maps, rudiments of intersection theory, divisors and the Riemann-Roch theorem for curves
None
Attendance will not be monitored, but you are strongly encouraged to attend class regularly and to take complete class notes
This course has a canvas page and this page will be used for posting homework assignments, announcements and various materials
Homework assignments with due dates are posted on the canvas page of our course. You may work together on homework assignments, but I expect everybody to write up their own solutions. The writing component is an important part of this course. Please justify all steps in your solutions of homework exercises. Please, write legibly. I may lower your score for not justifying steps in your solutions or for not writing legibly. The lowest grade for the homework assignment will be dropped.
You will need to present your solutions of 2-3 homework exercises. Alternatively, your presentation may consist of a proof of a theorem and a solution to a homework exercise. Examples of theorems include: the description of the category of affine varieties over a fixed algebraically closed field; the description of the category of varieties with morphisms being dominant rational maps; the characterization of a non-singular point in terms of its local ring; the characterization of the set of singular points as a proper closed subset; the Bezout theorem for plane projective curves; computation of the divisor class group for the product of projective spaces; Riemann-Roch theorem for a non-singular projective curve. The grade for your presentation will depend on the mathematical correctness, the clarity and your responses to questions. We may need to schedule some of your presentations outside of the regular class time.
93-100 A, 90-92 A-, 87-89 B+, 83-86 B, 80-82 B-, 70-79 C, 50-69 D, below 50 F
To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.
It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse.
Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.
During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).
The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.
The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).
The following academic support services are available to students (all links open in a new tab/window):
The Math Consulting Center
Student Success Center
University Libraries
Undergraduate Research Support
Career Center
Tuttleman Counseling Services
Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.