Reading seminar in algebraic geometry
Fall 2013. Toric varieties.

This semester the reading seminar will study toric varieties. Toric varieties are geometric spaces which have applications in algebraic geometry, symplectic geometry, representation theory, and combinatorics. They can be studied with few prerequisites in a combinatorial way, and can be used as an introduction to some basic notions of algebraic geometry.

The seminar will consist of introductory talks by faculty followed by talks by graduate students. We will attempt to make the seminar accessible to everyone.

The seminar will meet on Mondays at 3:00PM-4:00PM in LGRT 1334.



Schedule

Sept 6. Organizational meeting, 4:15PM, LGRT 1634.

Sept 16. Paul Hacking, UMass. What is a toric variety? 3:00PM, LGRT 1334.

Sept 23. David Cox, Amherst College. The toric variety of a fan. 3:00PM, LGRT 1334.

Sept 27. Jessica Sidman, Mt. Holyoke College. Toric varieties and polytopes. 4:00PM, LGRT 1634. (Note we are meeting on Friday.)

Oct 7. Eduardo Cattani, UMass. Divisors in toric varieties. 3:00PM, LGRT 1334.

Oct 15. Stephen Coughlan, UMass. Resolution of toric surface singularities. 3:00PM, LGRT 1334. (Note we are meeting on Tuesday, which is a "UMass Monday", due to Columbus day.)

Oct 21. No meeting.

Oct 28. Paul Hacking, UMass. Resolution of toric surface singularities. II. 3:00PM, LGRT 1334.

Nov 4. David Cox, Amherst college. The quotient construction of toric varieties. 3:00PM, LGRT 1334

Nov 13. Nikolay Buskin, UMass. Toric varieties: The symplectic viewpoint. 3:00PM, LGRT 1334. (Note we are meeting on Wednesday, which is a "UMass Monday", due to Veteran's day.)

Nov 18. Huy Le, UMass. Compactification of the universal elliptic curve. 3:00PM, LGRT 1334.

Nov 25. Tassos Vogiannou, UMass. Spherical varieties. 3:00PM, LGRT 1334.



References

Introductory references:

D. Cox, "What is a toric variety?". pdf.

D. Cox, "Introduction to algebraic geometry". pdf.

Expository texts:

D. Cox, J. Little, H. Schenck, Toric varieties. googlebooks.

W. Fulton, Introduction to toric varieties. googlebooks.

N. Proudfoot, Lectures on toric varieties. pdf. (These notes discuss the symplectic viewpoint.)

M. Atiyah, Angular momentum, convex polyhedra and algebraic geometry, Proc. Edinburgh Math. Soc. (2) 26 (1983), no. 2, 121--133. pdf. (Brief survey of moment maps and connections to algebraic geometry.)

Additional references:

M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1--15. pdf. (Original article describing the polytope associated to a (Hamiltonian) torus action on a symplectic manifold. Note: This result was also obtained independently by Guillemin and Sternberg.)

G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal embeddings I, Lecture Notes in Math. 339, Springer, 1973. Springer. (This is the original text on the algebraic theory.)

I. Gel'fand, M. Kapranov, A. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhauser, 1994. Springer. (This is the original text describing the "secondary polytope" and the geometric interpretation in terms of toric varieties.)



Links to the seminar from previous years.

Derived categories in algebraic geometry, Spring 2013
Deformation theory, Fall 2012
Curves, K3 surfaces, and Fano 3-folds, Spring 2012
Topics in algebraic geometry, Fall 2011
Surfaces of general type, Spring 2011
Algebraic surfaces, Fall 2010
Stability conditions on derived categories and wall crossing, Spring 2010
Mirror symmetry and tropical geometry, Fall 2009
Deformation theory, Fall 2008
Green's Conjectures, Spring 2008
Bridgeland Stability, Fall 2007
Minimal Model Program, Spring 2007
Commutative Algebra and Polyhedra Seminar, Spring 2006
Geometry and Algebra of Polyhedra Seminar, Fall 2005
Commutative Algebra Seminar, 2004-2005


The page is maintained by Paul Hacking