Introduction to Algebraic Geometry

 

A-B-C-D Term, Fall 2016 through Spring 2017

Intstructor: Maria Hempel

Time: Mondays, 3-4pm

Place: SL 405

Content

 

Algebraic geometry is one of the oldest and finest fields of geometry, with beautiful classical and modern techniques. It deals with the solution sets of sets of polynomial equations, and is both rich in its own right, and richly connected to other fields. Students completing this independent study project will be well equipped to go on to study algebraic geometry as pioneered by Grothendieck, arithmentic groups and number theory. It can also be seen as a theoretical prerequisite for advanced computer algebra. We will be reading Shafarevic's classic introduction Basic Algebraic Geometry and collectively solve all the exercises. To do so we will join forces in a collective project on sagemathcloud and in passing get familiarized with LaTeX. Students are encouraged to learn the relevant computer algebra for experimentation, and even more encouraged to practice the traditional art of staring into the air with several imaginary pairs of disconnected eye visions. The two books are subdivided into a total of four chapters, each of which we'll adress in one term.

 

Prerequisites

 

The ISP is most suitable for mathematics graduate students as well as eager senior and junior undergraduates, and possible for brave sophomores. We do exepct a serious commitment to the project. Courses in abstract algebra such as Group Theory, and Rings and Fields are of great advantage, as are any proof-based courses. Conceptionally oriented computer scientists are also very welcome.

 

Literature

 

Main Reference

Additional Resources

  • Algebraic Curves, William Fulton, freely available via link
  • Undergraduate Algebraic Geometry, Miles Reid, LMS Student Texts 12
  • Undergraduate Commutative Algebra, Miles ReidLMS Student Texts 29
  • Ideals, Varieties, and AlgorithmsCox, Little, O'Shea, Springer Undergratuate Texts in Mathematics, available via WPI
  • Computational Algebraic Geometry, Hal Schenk, LMS Student Texts 68 

Sitting on your shelf for reference

  • Principles of Algebraic Geometry, Griffiths&Harris
  • Algebraic TopologyWilliam Fulton, Springer Graduate Texts in Mathematics, available via WPI

Suggested future reading