Algebraic Geometry / Commutative Algebra Seminar
Spring 2008
Green's Conjecture
The working AG/CA seminar will be devoted to syzygies of curves.
We will try to make everything accessible to graduate students
who take the class in algebraic geometry.
So essentially this will be one long exercise on applying basic tools of Algebraic Geometry.
This will dictate the choice of material but the hope (probably too optimistic)
is to understand at least the most basic ideas and insights
behind the recent proof of Green's Conjecture by Claire Voisin.
As usual, everybody is wellcome to contribute talks.
Dates:
Feb 8. Jessica Sidman. Resolutions and Syzygies - 1.
Feb 15. Jessica Sidman. Resolutions and Syzygies - 2.
Feb 22. Jessica Sidman. Resolutions and Syzygies - 3.
Feb 29. Jessica Sidman. Resolutions and Syzygies - 3 (rescheduled).
Mar 7. Jenia Tevelev. Algebraic Curves - 1.
Mar 14. Jenia Tevelev. Algebraic Curves - 2.
Mar 21. No seminar - spring break
Mar 28. Eyal Markman. K3 Surfaces -1 .
Apr 4. Eyal Markman. K3 Surfaces - 2.
Apr 11. Eyal Markman. K3 Surfaces - 3. Sukhendu Mehrotra. Petri-Gieseker following Lazarsfeld - 1.
Apr 18. Sukhendu Mehrotra. Petri-Gieseker following Lazarsfeld - 2.
Apr 25. Jenia Tevelev. Generic Green's Conjecture (following Claire Voisin) - 1.
May 2. Jason Brunson. Bertini Theorem. Adam Gamzon. Petri's Theorem.
May 9. Jenia Tevelev. Generic Green's Conjecture (following Claire Voisin) - 2.
Some references and links:
David Eisenbud, Lectures on the geometry of syzygies,
with a chapter by Jessica Sidman. 38 pages. Trends in commutative algebra. MSRI Publications. 51 (2004), 115-152
David Eisenbud,
Green's conjecture: An orientation for algebraists, 28 pages,
Research Notes in Mathematics. 2 (1992), 51-78
Rob Lazarsfeld, Brill-Noether-Petri without degenerations, J.Diff.Geom. 23, 299-307 (1986)
Another proof is in:
Giuseppe Pareschi, A proof of Lazarsfeld's theorem on curves on $K3$ surfaces
J. Algebraic Geom. 4 (1995), no. 1, 195--200
Mark Green, Koszul cohomology and the geometry of projective varieties, J.Diff.Geom. 19, (1984) 125-171
Arnaud Beauville,
La conjecture de Green generique [d'apres C. Voisin], S´eminaire BOURBAKI, Novembre 2003,
56`eme ann'ee, 2003-2004, no. 924
M. Teixidor I Bigas, Green's conjecture for the generic r-gonal curve
of genus g\ge 3r-7, Duke Math. J. 111:2 (2002), 195-222
Clair Voisin,
Green's generic syzygy conjecture for curves of even genus lying on a K3 surface,
J. Eur. Math. Soc. 4:4 (2002), 363-404
Clair Voisin,
Green's canonical syzygy conjecture for generic curves of odd genus,
Compos. Math. 141 (2005), no. 5, 1163-1190
Below are links to the seminar from previous years.
Bridgeland Stability Seminar,
Fall 2007
Minimal Model Program Seminar,
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 Jenia Tevelev