MAT 614 — Fall 2014 Problem Sets MAT 614 — Fall 2014 Syllabus

MAT 614 Course Webpage
Topics in Algebraic Geometry: Intersection Theory
Tu Th 1PM — 2:20PM, Earth Space Sciences 177

Fall 2014

  • Problem sets
  • Syllabus

  • Course Announcements
  • Course Description
  • Prerequisites
  • Text
  • Lectures
  • Office Hours
  • Disability Support Services
  • Academic Integrity
  • Critical Incident Management

  • 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 Dating back to Schubert, Chasles, Zeuthen, etc. in the 1800s, intersection theory is the study of intersections of cycles in algebraic varieties. Originally a tool for solving enumerative algebraic geometry -- still one of the most important applications -- it has now grown beyond that, with connections to K-theory, Hodge theory, etc. I will explain the basic theory, with emphasis on examples and computations, through the celebrated Grothendieck-Riemann-Roch theorem, an algebraic analogue of the index theorem. The only prerequisite is a basic understanding of algebraic geometry.

    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. I recommend the following two excellent textbooks.

    Time permitting, I would also like to discuss some additional topics, possibly from among the following: equivariant intersection theory, intersection theory for stacks, construction of the virtual fundamental class, quantum cohomology / Chow theory / K-theory.

    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, 1:00 PM — 2:20PM in Earth Space Sciences 177.

    Office Hours

    Grading System As discussed at the first class meeting, grading will be based on class participation.

    Disability Support Services If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, 128 ECC Building (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

    Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following web site: and search Fire Safety and Evacuation and Disabilities.

    Academic Integrity 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 are 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

    Critical Incident Management 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, and/or inhibits students' ability to learn.

    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