Algebraic Geometry
Math 9053L: Algebraic Geometry
Summer 2025
Meeting Times and location: See student centre
Office Hours: WF: after class
Marks: Final exam worth 50%
4 assignments worth 12.25% each. (submitted online using gradescope.ca)
Assignments will be due approximately every two weeks.
Homework is due at 11pm on specified days. Late homework will be accepted upto 72hours past the official due date with no penalty.
Instructor: Ajneet Dhillon adhill3@uwo.ca
Syllabus: Affine and projective varieties. Decompositions in the Zariski topology. Bezout's theorem and Hilbert functions.
Required Textbook: None. Notes will be provided. All course material will be hosted on owl.uwo.ca
Supplementary texts: B.Hasset "Introduction to algebraic geometry"
D. Eisenbud "Commutative algebra with a view toward algebraic geometry"
I. Shaferevich "Basic algebraic geometry"
Prerequisites: Successful completion of Math 4123, "Rings and Modules"
Learning Outcomes:
- Be able to define and list the main properties of affine varieties
- Understand and use the coordinate ring to study morphisms of affine varieties
- Define the notion of a projective variety
- Define and compute intersection multiplicities
- Understand irreducible and primary decompositions
- Be able to state and apply Bezout's theorem in the plane.
Senate Policy on Prerequisites
Unless you have either the requisites for this course or written special permission from your Dean to enroll in it, you may be removed from this course and it will be deleted from your record. This decision may not be appealed. You will receive no adjustment to your fees in the event that you are dropped from a course for failing to have the necessary prerequisites.
Course Websites
Students should check OWL brightspace regularly.
Accommodation and Accessibility
If you are unable to meet a course requirement due to illness or other serious circumstances, you must seek approval for the absence as soon as possible. Approval can be granted either through a self-reporting of absence or via the Dean’s Office/Academic Counselling unit of your Home Faculty. If you are a Science student, the Academic Counselling Office of the Faculty of Science is located in NCB 280, and can be contacted at scibmsac@uwo.ca.
For further information, please consult the university’s policy on academic consid-eration for student absences: https://www.uwo.ca/univsec/pdf/academic_policies/ appeals/Academic_Consideration_for_absences.pdf.
If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you are able to do so. They will assess your eligibility to write the Special Exam (the name given by the university to a makeup Final Exam).
You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation” (see http://www.registrar.uwo.ca/examinations/exam_ schedule.html).
Academic Policies
In accordance with policy, http://www.uwo.ca/its/identity/activatenonstudent.html, the centrally administered e-mail account provided to students will be considered the individual's official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.
Students must use their Western (@uwo.ca) email addresses when contacting their instructors.
Electronic devices (including cell phones, ipods and calculators) are NOT allowed on exams and may be confiscated.
Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at the following Web site: http://www.uwo.ca/univsec/pdf/academic_policies/appeals/scholastic_discipline_undergrad.pdf.
In the event of a health lockdown, tests and examinations in this course will be conducted using a remote proctoring service. By taking this course, you are consenting to the use of this software and acknowledge that you will be required to provide personal information (including some biometric data) and the session will be recorded. Completion of this course will require you to have a reliable internet connection and a device that meets the technical requirements for this service. More information about this remote proctoring service, including technical requirements, is available on Western’s Remote Proctoring website at:
https://remoteproctoring.uwo.ca.
Student Absences
If you are unable to meet a course requirement due to illness or other serious circumstances, please follow the procedures below:
Assessments worth less than 10% of the overall course grade:
Please contact your instructor as soon as possible to seek accommodation. Note that these assessments have built in allowances for short term illnessess. Typically no extra allowances will be granted.
Assessments worth 10% or more of the overall course grade:
For work totalling 10% or more of the final course grade, you must provide valid medical or supporting documentation to the Academic Counselling Office of your Faculty of Registration as soon as possible. For further information, please consult the University’s medical illness policy at
https://www.uwo.ca/univsec/pdf/academic_policies/appeals/accommodation_medical.pdf
The Student Medical Certificate is available at
https://www.uwo.ca/univsec/pdf/academic_policies/appeals/medicalform.pdf
Accommodation and Accessibility
Religious Accommodation
When a course requirement conflicts with a religious holiday that requires an absence from the University or prohibits certain activities, students should request accommodation for their absence in writing at least two weeks prior to the holiday to the course instructor and/or the Academic Counselling office of their Faculty of Registration. Please consult University's list of recognized religious holidays (updated annually) at
https://multiculturalcalendar.com/ecal/index.php?s=c-univwo.
Accommodation Policies
Students with disabilities are encouraged to contact Accessible Education, which provides recommendations for accommodation based on medical documentation or psychological and cognitive testing. The policy on Academic Accommodation for Students with Disabilities can be found at:
https://www.uwo.ca/univsec/pdf/academic_policies/appeals/Academic Accommodation_disabilities.pdf.
Support Services
Please visit the Science & Basic Medical Sciences Academic Counselling webpage for information on adding/dropping courses, academic considerations for absences, appeals, exam conflicts, and many other academic related matters: https://www.uwo.ca/sci/counselling/.
Students who are in emotional/mental distress should refer to Mental Health@Western (https://uwo.ca/health/) for a complete list of options about how to obtain help.
Western is committed to reducing incidents of gender-based and sexual violence and providing compassionate support to anyone who has gone through these traumatic events. If you have experienced sexual or gender-based violence (either recently or in the past), you will find information about support services for survivors, including emergency contacts at https://www.uwo.ca/health/student_support/survivor_support/get-help.html. To connect with a case manager or set up an appointment, please contact support@uwo.ca.
Please contact the course instructor if you require lecture or printed material in an alternate format or if any other arrangements can make this course more accessible to you. You may also wish to contact Accessible Education at http://academicsupport.uwo.ca/accessible_education/index.html if you have any questions regarding accommodations.
Learning-skills counsellors at the Student Development Centre (https://learning.uwo.ca) are ready to help you improve your learning skills. They offer presentations on strategies for improving time management, multiple-choice exam preparation/writing, textbook reading, and more. Individual support is offered throughout the Fall/Winter terms in the drop-in Learning Help Centre, and year-round through individual counselling.
Western University is committed to a thriving campus as we deliver our courses in the mixed model of both virtual and face-to-face formats. We encourage you to check out the Digital Student Experience website to manage your academics and well-being: https://www.uwo.ca/se/digital/.
Additional student-run support services are offered by the USC, https://westernusc.ca/services/.