Reading seminar in algebraic geometry
Spring 2012. Curves, K3 surfaces, and Fano 3-folds.

This semester the reading seminar will study the description of Fano 3-folds as linear sections of homogeneous spaces obtained by Mukai. This is related to Mukai's work on vector bundles over K3 surfaces and explicit models for curves of low genus. More recently Kuznetsov has used Mukai's results to study the derived category of Fano 3-folds.

The seminar will consist of introductory talks by faculty followed by talks by graduate students. Applications to the derived category will be discussed towards the end after some of the necessary tools have been developed in Jenia Tevelev's class (course webpage). We will attempt to make the seminar accessible to everyone.

The seminar will meet on Fridays at 2:45PM-3:45PM in LGRT 1634. We will also have a few meetings on Thursdays to accommodate speakers with teaching commitments on Fridays.



Schedule

Jan 27. Organizational meeting, 3:15PM, LGRT 1634.
Feb 3. Paul Hacking, UMass. Curves, K3 surfaces, and Fano 3-folds. 2:45PM, LGRT 1634. Abstract. Lecture notes by Anna Kazanova pdf.
Feb 10. Eyal Markman, UMass. A few basic facts about K3 surfaces. 2:45PM, LGRT 1634.
Feb 16. Jeremy Pecharich, Mt Holyoke. An introduction to noncommuative algebraic geometry 'in the small'. (Thursday pre-talk for VGS.) 2:45PM, LGRT 1634.
Feb 17. Stephen Coughlan, UMass. Fano 3-folds after Fano and Iskovskikh. 2:45PM, LGRT 1634.
Feb 24. Alexei Oblomkov, UMass. Fano 3-folds after Fano and Iskovskikh II. 2:45PM, LGRT 1634.
Mar 2. Alexei Oblomkov, UMass. Fano 3-folds after Fano and Iskovskikh III. 2:45PM, LGRT 1634.
Mar 9. Jenia Tevelev, UMass. Mukai Models I, G2 and K3. 2:45PM, LGRT 1634.
Mar 16. Jenia Tevelev, UMass. Mukai Models II. 2:45PM, LGRT 1634.
Mar 23. Spring Break.
Mar 30. No meeting due to AGNES.
Apr 6. Bradley Willocks, UMass. Which K3 surfaces are anticanonical divisors on Fano threefolds? (after Beauville). 2:45PM, LGRT 1634.
Apr 13. Anna Kazanova, UMass. On the moduli space of bundles on K3 surfaces. 2:45PM, LGRT 1634.
Apr 26. Rina Anno, UMass. Derived categories of Fano 3-folds. 3:00PM, LGRT 1634.
Apr 27. Julie Rana, UMass. Which Fuchsian singularities are smoothable? (after Nikulin, Pinkham, Dolgachev, and Looijenga). 2:45PM, LGRT 1322.


References

S. Mukai, Curves, K3 surfaces and Fano 3-folds of genus <= 10, in Algebraic geometry and commutative algebra, Vol. I, 357-377, Kinokuniya, Tokyo, 1988. pdf

S. Mukai, On the moduli space of bundles on K3 surfaces. I, in Vector bundles on algebraic varieties (Bombay, 1984), 341-413, Tata Inst. Fund. Res. Stud. Math., 11, Tata Inst. Fund. Res., Bombay, 1987. pdf

A. Kuznetsov, Derived categories of Fano 3-folds, Proc. Steklov Inst. Math. 264 (2009), no. 1, 110-122 and preprint arXiv:0809.0225v1 [math.AG] arXiv.

V. Iskovskih, Fano 3-folds, I and II, part I, Math. USSR-Izv. 11 (1977), no. 3, 485--527 (1978) pdf; part II, ibid. 12 (1978), no. 3, 469--506 (1979) pdf.



Links to the seminar from previous years.

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