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.

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

Sept 16. Paul Hacking, UMass.

Sept 23. David Cox, Amherst College.

Sept 27. Jessica Sidman, Mt. Holyoke College.

Oct 7. Eduardo Cattani, UMass.

Oct 15. Stephen Coughlan, UMass.

Oct 21. No meeting.

Oct 28. Paul Hacking, UMass.

Nov 4. David Cox, Amherst college.

Nov 13. Nikolay Buskin, UMass.

Nov 18. Huy Le, UMass.

Nov 25. Tassos Vogiannou, UMass.

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