Summer Graduate School

This simplicial fan in 3-dimensional space

Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

For eligibility and how to apply, see the Summer Graduate Schools homepage

Suggested Prerequisites:

• Chapters 1,2,3,4,5,8 of "Ideals, Varieties and Algorithms" and Sections 1.0, 2.0, 3.0, 4.0 and 6.0 of "Toric Varieties" (Section 0 of these chapters is a background section that discusses algebraic geometry with no knowledge of toric varieties required).  An alternative to the Sections 0 would be my notes "Introduction to Algebraic Geometry", available at my web site https://dacox.people.amherst.edu/.
• Chapters 1,2,3,4 of Ravi Vakil's excellent text "Foundation of Algebraic Geometry", freely available at math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf
• Chapters 1 and 2 of Hartshorne's "Algebraic Geometry".

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.