MAT 615. Introduction to Algebraic Geometry
Samuel Grushevsky, Spring 2012, Stony Brook University
TuTh 2:20pm - 3:40pm, in Physics P112

Overview: The course will be an introduction to modern algebraic geometry. We will mostly concentrate on sheaves, schemes, and sheaf cohomology. The material covered will be comparable to chapters II and III of Hartshorne, though different textbooks will be used (see below). The geometric aspects of the theory will be emphasized throughout, and numerous examples provided. The goal is to develop familiarity with concepts so that you could work with them comfortably in a geometric context.

Prerequisites: Some exposure to complex or algebraic manifolds will be implicitly assumed, though we'll start with Nullstellensatz. MAT 545 (Complex Geometry/Griffiths-Harris) is certainly sufficient preparation. Some results from commutative algebra will be used as black boxes. If in doubt, please ask me.

Grading: Please see me if you have not passed your orals yet.

Textbook: While there is no one textbook, we will use much material and structure from Ravi Vakil's Lecture notes. Ravi welcomes any suggestions, found typos, etc. - please contact him directly, or I am happy to aggregate comments and forward. We will also use some material from Mumford's The Red Book of Varieties and Schemes, and from Eisenbud and Harris' The Geometry of Schemes.

Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. 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.

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