Spring 2014. Syzygies.

This semester the reading seminar will study syzygies. Roughly speaking, given an algebraic variety, its defining equations typically satisfy non-trivial relations, called syzygies. The interplay between the commutative algebra of syzygies and the geometric properties of the variety is a basic topic in 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 1322.

Jan 24. Organizational meeting, 3:30PM, LGRT 1234.

Feb 3. Jessica Sidman, Mt. Holyoke College.

Feb 10. Paul Hacking, UMass.

Feb 18. Stephen Coughlan, UMass.

Feb 24. Jennifer Biermann, Mt. Holyoke College.

Mar 3. No meeting.

Mar 10. David Cox, Amherst College.

Mar 17. No meeting (Spring break).

Mar 24. Huy Le, UMass.

Mar 31. Morgan Opie, UMass.

Apr 7. Tassos Vogiannou, UMass.

Apr 14. Zhijie Dong, UMass.

Expository texts:

D. Eisenbud, "Commutative algebra with a view toward algebraic geometry", Grad. Texts in Math. 150, Springer, 1995.

D. Eisenbud, "The geometry of syzygies". SpringerLink (freely accessible via UMass).

D. Mumford, "Varieties defined by quadrics". pdf.

Research articles:

D. Buchsbaum and D. Eisenbud, "Gorenstein ideals of height 3". pdf.

L. Ein and R. Lazarsfeld, "Asymptotic syzygies of algebraic varieties". SpringerLink (freely accessible via UMass).

Links to the seminar from previous semesters.

Toric varieties, Fall 2013

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