Math 591– Algebraic Geometry
        Fall 2011, MWF 10:15–11:05 AM, 1220 SAS Hall
        Instructor: Seth Sullivant, office: SAS Hall 3114, email: smsulli2@ncsu.edu
        Office Hours: W 1:30-2:30 PM, Th 2:30-3:30 PM
        Text: B. Hassett, Introduction to Algebraic Geometry, Cambridge University Press, 2007,
        ISBN-13: 978-0521691413
        Additional Reading: Cox, Little, and O’Shea, Ideals, Varieties, and Algorithms; Eisenbud
        and Harris, The Geometry of Schemes; Hartshorne, Algebraic Geometry
        Course Website: http://www4.ncsu.edu/~smsulli2/MA591 Fall2011/MA591.html
        CourseDescription: Algebraicgeometryisthestudyofsolutionstosystemsofpolynomial
        equations. The algebra/geometry dictionary establishes a bijection between such solution
        sets and certain ideals in a polynomial ring. Hence, techniques from commutative algebra
        can be used to analyze these geometric objects. The course will provide an introduction
        to algebraic geometry. We will emphasize not only the theory, but also practical aspects of
        how to compute with polynomial ideals using Groebner bases. We will discuss the following
        topics: ideals and affine varieties, the Nullstellensatz, irreducible varieties and primary de-
        composition, morphisms and rational maps, Grbner bases and elimination theory, projective
        varieties, Grassmannians, graded modules, Hilbert functions, Bezout’s theorem.
        Homework: Homework will be assigned regularly in the first half of the semester and is
        due in class on Fridays. Students must write up their own solutions. Please indicate on your
        homework any sources that you used in preparing solutions (e.g. if another student helped
        with a solution, or you found the solution in a book). Students are encouraged to prepare
        homework solutions in LateX. Homework assignments can be found at the course website as
        well as information on preparing your homework in LateX.
        Exams: There will be one take home midterm exam, and an in-class final exam. The final
        exam will take place in the usual classroom 8:00-11:00 AM, December 7th.
        Grades: GradeswillbebasedonHomework(70%),Midterm(10%),andFinalExam(20%).
        Attendance: Students are expected to arrive on time, to contribute to group work and
        class discussions, and to stay until the class ends.
        Adverse Weather: Announcements regarding scheduled delays or the closing of the Uni-
        versity due to adverse weather conditions will be broadcast on local radio and television
        stations and posted on the University homepage.
        Cell Phones: Pagers, cellular phones and other types of telecommunication equipment are
        prohibited from use during class. Make sure that any pagers, phones or other equipment are
        turned off during the class period. If you have a special need to have your pager or phone
        on during class, please let me know.
        Academic Integrity Statement: Students are required to follow the NCSU policy . Aca-
        demic dishonesty is the giving, taking, or presenting of information or material by a student
        that unethically or fraudulently aids oneself or another on any work which is to be considered
        in the determination of a grade or the completion of academic requirements or the enhance-
        ment of that student’s record or academic career. (NCSU Code of Student Conduct). The
        Student Affairs website has more information.
       Students with Disabilities: Reasonable accommodations will be made for students with
       verifiable disabilities. In order to take advantage of available accommodations, students must
       register with Disabilities Services for Students.
       Class Evaluations: Online class evaluations will be available for students to complete
       during the last two weeks of class. Students will receive an email message directing them to
       awebsitewheretheycanloginusingtheirUnityIDandcompleteevaluations. Allevaluations
       are confidential; instructors will never know how any one student responded to any question,
       and students will never know the ratings for any particular instructors.