Math 547, Algebraic Geometry I - Fall 2017

Instructor: Jack Huizenga

Jack Huizenga
Office: 324 McAllister
email: huizenga@psu.edu
URL: http://www.personal.psu.edu/jwh6013/
  • Meeting times: MWF 12:20-1:10, 113 Osmond
  • First meeting: Monday, August 21
  • Office hours: Monday 4-5, or by appointment. (Subject to change based on student availability)
  • Textbooks: We will begin primarily with "Basic Algebraic Geometry I" by Shafarevich. As the course progresses we will supplement many subjects with material from "Algebraic Geometry: A First Course" by Harris.
Brief course description: The course will be an introduction to the theory of affine and projective varieties over an algebraically closed field. We will cover topics such as regular and rational functions, morphisms, dimension, degree, smoothness and singularities. Emphasis will be placed on important concrete examples of varieties, such as Grassmannians, Fano varieties, incidence correspondences, and varieties of small degree.
Prerequisites: Familiarity with algebra (especially commutative algebra) at the level of Math 536 - Abstract Algebra will be assumed. Since Math 538 - Commutative Algebra was offered last term, we will assume some major results from commutative algebra (e.g. the Hilbert Basis Theorem and Nullstellensatz) without proof. Students missing this background will be given resources to catch up. While proofs of these results will not be given, the relevance of these results to algebraic geometry will certainly be explored.
Homework: There will be approximately 7 problem sets of roughly 10 problems each, due at the beginning of class every other Wednesday. Roughly 2 of the exercises on each set will be marked with a "star," indicating that the problem is especially relevant. I strongly encourage all students to complete the homework, especially if algebraic geometry is likely to be relevant to your eventual research specialty. This material is challenging, and it is not possible to learn the subject "by osmosis." However, I understand that you have many competing demands on your time (especially as you progress in your Ph.D. studies). You are all adults, so you may determine your own goals for the course and complete the homework accordingly.
  • To achieve working proficiency in algebraic geometry you should complete all the homework on time, in order to keep up with the class.
  • To become acquainted with some of the basic ideas of algebraic geometry, you should at a minimum complete the starred exercises by the end of the semester. (If you fall into this group it may be particularly helpful to work with others.)
  • If you already have substantial prior experience with algebraic geometry, it might be most appropriate to look at the exercises and verify for yourself that you know the key insights.
Late work will be accepted, but will be marked for completion only. Students are encouraged to work on the problems together as desired, but your final writeup must be completed independently.
Grading and Expectations: Your grade will be based on a combination of your homework and attendance.
Academic Integrity Statement: All Penn State policies regarding ethics and honorable behavior apply to this course.
Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. The Office for Disability Services Web site provides contact information for every Penn State campus: http://equity.psu.edu/ods/dcl . For further information, please visit the Office for Disability Services Web site: http://equity.psu.edu/ods .
Homework assignments :
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