Toric varieties
References:
- G. Barthel, L. Bonavero, M. Brion, D. Cox, Notes of the summer school Geometry of toric varieties, Grenoble, 2000.
- D. Cox, J.B. Little, H.K. Schenck, Toric varieties, Graduate Studies in Mathematics, vol. 124, American Mathematical Society, Providence, RI, 2011.
- V. Danilov, The geometry of toric varieties, Russian Math. Surveys 33 (1978).
- W. Fulton, Introduction to toric varieties, Ann. of Math. Stud., vol. 131, Princeton University Press, Princeton, NJ, 1993.
- M. Mustata, Lecture notes on toric varieties, 2005
Suggested seminars:
- The Cox ring of a toric variety
- The equivariant cohomology ring of a smooth complete toric variety
- The Nef cone and the Mori cone
- Mixed volumes and Bernstein-Koushnirenko theorem
- The algebraic moment map and the non-negative part of a toric variety
- [Cox, Little, Schenck], Chapter 12.2
- [Fulton], Chapter 4.1, 4.2
- F. Sottile, Toric ideals, real toric varieties, and the algebraic moment map, Sections 6, 7, 8
- Smooth toric surfaces
- [Cox, Little, Schenck], Chapter 8.3, 10.4, 10.5
- D. Cox, Toric surfaces, Notes of the summer school of Grenoble
- Groebner fans, minimal resolutions and McKay correspondence in dimenson 2
- Riemann-Roch theorem and integral points in convex polytopes
Some broader topics which can be covered by more than one seminar are also
- Symplectic toric manifolds
You can also propose some other argument, these surveys of Cox may suggest you other possibilities