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MAT 614 Course Webpage
Topics in Algebraic Geometry: A Second Course in Algebraic Geometry
Tu Th 11:30AM — 12:50PM, Physics P—127
Fall 2023
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Course Announcements
Announcements about the course will be posted here. Please check the
site regularly for announcements (which will also be given in lecture
and/or in recitation).
Course
Description
How do we use the language of varieties, schemes, sheaves and
cohomology to solve the type of algebraic geometry problem that arises
often in pure mathematics? This course will survey and illustrate a
number of techniques for using algebraic geometry to solve problems:
intersection theory, parameter spaces, moduli spaces, algebraic
stacks, Hodge theory, deformation theory, etc. The choice of topics
will be finalized with input from the students.
Prerequisites
Students should have passed the graduate algebra sequence. A basic
understanding of the language of modern algebraic geometry will also
be essential.
Text
There is no required textbook. Our approach will be to survey
techniques with only a brief overview of proofs, but with links to the
literature. The list of references will grow as the semester progresses.
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A. J. de Jong and others, The Stacks Project.
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William Fulton Intersection Theory, 2nd ed.
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Eisenbud, D. and Harris, J. 3264 and all that.
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Fantechi, B., et al., FGA Explained.
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Bosch, S., Lutkebohmert, W., and Raynaud, M., Neron models.
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Mumford, D., Geometric invariant theory.
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Knutson, D., Algebraic spaces.
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Artin, M., Grothendieck topologies.
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Laumon, G., and Moret-Bailly, L., Champs algebriques.
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Olsson, M., Algebraic stacks.
Lectures
The instructor for this course is
Jason Starr.
All instruction will occur in lectures. A tentative schedule will be posted
in the syllabus.
Lecture is held Tuesdays and Thursdays, 11:30 AM — 12:50PM in
Physics P—127.
Office Hours
Here is
a link
to the current office hours.
Grading System
As discussed at the first class meeting, grading will be based on
class participation.
If you have a physical, psychological, medical, or learning disability
that may impact your course work, please contact the Student
Accessibility Support Center, Stony Brook Union Suite 107, (631)
632-6748 or at sasc@Stonybrook.edu. They will determine with you what
accommodations are necessary and appropriate. All information and
documentation is confidential.
Student Accessibility Support Center
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and SASC. For
procedures and information go to the following website:
Evacuation guide for people with physical disablilities
Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing another
person's work as your own is always wrong. Faculty is required to
report any suspected instance of academic dishonesty to the Academic
Judiciary. For more comprehensive information on academic integrity,
including categories of academic dishonesty, please refer to the
academic judiciary website at
Academic
Judiciary
Stony Brook University expects students to respect the rights,
privileges, and property of other people. Faculty are required to
report to the Office of Judicial Affairs any disruptive behavior that
interrupts their ability to teach, compromises the safety of the
learning environment, or inhibits students' ability to learn.
Further information about most academic matters can be found in the
Undergraduate Bulletin, the Undergraduate Class Schedule, and the
Faculty-Employee Handbook.
Back to my home page.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr