MAT 614 Course Webpage
Topics in Algebraic Geometry: A Second Course in Algebraic Geometry
Tu Th 11:30AM 12:50PM, Physics P127
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).
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.
Students should have passed the graduate algebra sequence. A basic
understanding of the language of modern algebraic geometry will also
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.
A. J. de Jong and others, The Stacks Project.
William Fulton Intersection Theory, 2nd ed.
Eisenbud, D. and Harris, J. 3264 and all that.
Fantechi, B., et al., FGA Explained.
Bosch, S., Lutkebohmert, W., and Raynaud, M., Neron models.
Mumford, D., Geometric invariant theory.
Knutson, D., Algebraic spaces.
Artin, M., Grothendieck topologies.
Laumon, G., and Moret-Bailly, L., Champs algebriques.
Olsson, M., Algebraic stacks.
The instructor for this course is
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
to the current office hours.
As discussed at the first class meeting, grading will be based on
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
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Further information about most academic matters can be found in the
Undergraduate Bulletin, the Undergraduate Class Schedule, and the
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4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651