Reading seminar in algebraic geometry
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.



Schedule

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

Feb 3. Jessica Sidman, Mt. Holyoke College. Varieties and Syzygies. Abstract. 3:00PM, LGRT 1322.

Feb 10. Paul Hacking, UMass. Syzygies of curves of genus 0 and 1. 3:00PM, LGRT 1322.

Feb 18. Stephen Coughlan, UMass. Hilbert series and free resolutions. Abstract. 3:00PM, LGRT 1322. (Note we are meeting on Tuesday, which is a UMass Monday, due to Presidents' day.)

Feb 24. Jennifer Biermann, Mt. Holyoke College. Free resolutions of monomial ideals. 3:00PM, LGRT 1322.

Mar 3. No meeting.

Mar 10. David Cox, Amherst College. The Hilbert-Burch Theorem, Geometric Modeling, and a Multigraded Example. Abstract. 3:00PM, LGRT 1322.

Mar 17. No meeting (Spring break).

Mar 24. Huy Le, UMass. Resolution of the diagonal for projective space and classification of vector bundles on the projective plane. 3:00PM, LGRT 1322.

Mar 31. Morgan Opie, UMass. Koszul quadratic algebras - I. 3:00PM, LGRT 1322.

Apr 7. Tassos Vogiannou, UMass. Koszul quadratic algebras - II. 3:00PM, LGRT 1322.

Apr 14. Zhijie Dong, UMass. The Buchsbaum-Eisenbud structure theorem for Gorenstein ideals of codimension 3. 3:00PM, LGRT 1322.




References

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