MAT 615 — Fall 2018 Problem Sets MAT 615 — Fall 2018 Syllabus

MAT 615 Course Webpage
Topics in Algebraic Geometry: Spaces of Curves on Algebraic Varieties
Tu Th 2:30PM — 3:50PM, Physics P—122

Fall 2018

  • 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 This course focuses on the most classical parameter spaces / moduli spaces in algebraic geometry: moduli spaces of curves and parameter spaces of curves in a fixed algebraic variety. In addition to introducing the foundational techiniques in algebraic geometry for working with such moduli spaces (Artin's algebraization theorems, Grothendieck-Riemann-Roch, ampleness criteria, connectedness theorems, etc.), we will focus on specific applications such as the following:

    The only prerequisite is an understanding of algebraic geometry at the level of a typical graduate textbook (algebraic geometry over fields other than the complex numbers plays a crucial role, even for proving theorems about complex varieties).

    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. For the first few weeks, I will present foundational theorems in the area (Mori's proof of Hartshorne's conjecture, the Kontsevich recursion formulas for genus 0 curves in the plane, boundedness of Fano manifolds, etc.). For general background, I recommend the following two excellent textbooks.

    Here is a list of some original articles that will be important in the later part of the course.

    Lectures The instructor for this course is Jason Starr. All instruction will occur in lectures. The tentative schedule is in the syllabus.

    Lecture is held Tuesdays and Thursdays, 2:30 PM — 3:50PM in Physics P—122.

    Office Hours Office hours are to be announced.

    Grading System The grading system will be discussed at the first class meeting.

    Americans with Disabilities Act.
    If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center, ECC (Educational Communications Center) Building, Room 128, (631)632-6748. They will determine with you what accommodations, if any, 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 the Student Accessibility Support Center. For procedures and information go to the following website: 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 instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. 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 University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.

    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