Reading seminar in algebraic geometry

Spring 2013. Derived categories in algebraic geometry.

This semester the reading seminar will study derived categories of coherent sheaves on algebraic varieties.

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 Fridays at 2:40PM-3:45PM in LGRT 1634.

**Schedule**

Jan 25. Organizational meeting, 3:15PM, LGRT 1634.

Feb 1. Paul Hacking, UMass. *Derived categories in algebraic geometry*. 2:40PM, LGRT 1634.

Feb 13. Ivan Mirkovic, UMass. *Representations of quivers in algebraic geometry*. 4:00PM, LGRT 1322. (Note unusual date and time. This seminar has been rescheduled due to weather.)

Feb 15. Alexei Oblomkov, UMass. *Fourier--Mukai transforms for abelian varieties*. 2:40PM, LGRT 1634.

Feb 22. Stephen Coughlan, UMass. *Exceptional collections on Enriques surfaces*. 2:40PM, LGRT 1634.

Mar 1. Eyal Markman, UMass. *Equivalences of derived categories of K3 surfaces*. Abstract. 2:40PM, LGRT 1634.

Mar 8. Jenia Tevelev, UMass. *Phantom Categories*. Abstract. 2:40PM, LGRT 1528. Note special room.

Mar 15. Anna Kazanova, UMass. *Exceptional collections on del Pezzo surfaces*. 2:40PM, LGRT 1634.

Mar 22. Spring Break.

Mar 29. Tassos Vogiannou, UMass. *Variations of Hodge structure*. 2:40PM, LGRT 1634.

Apr 5. No seminar.

Apr 12. Nikolay Buskin, UMass. *Torelli theorem via Fourier-Mukai transform*. 2:40PM, LGRT 1634.

Apr 19. No seminar due to AGNES.

Apr 26. Huy Le, UMass. *Some standard equivalences of derived categories of coherent sheaves*. Abstract. 2:40PM, LGRT 1634.

**References**

Introductory references:

Jenia's class on homological methods here.

A. Caldararu, *Derived categories of sheaves: A skimming*. arXiv.

R. Thomas, *Derived categories for the working mathematician*. arXiv.

D. Huybrechts, *Fourier--Mukai transforms in algebraic geometry*. ebrary. (freely available via UMass).

Research papers:

D. Auroux, L. Katzarkov, D. Orlov, *Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves*, Invent. Math. 166 (2006), no. 3, 537--582.
journal, arXiv.

A. Beilinson, A. Polishchuk, *Torelli theorem via Fourier-Mukai transform*, in Moduli of abelian varieties (Texel Island, 1999), 127--132,
Progr. Math., 195, Birkhauser, Basel, 2001. arXiv.

T. Bridgeland, D. Stern, *Helices on del Pezzo surfaces and tilting Calabi-Yau algebras*, Adv. Math. 224 (2010), no. 4, 1672--1716. journal, arXiv.

S. Galkin, E. Shinder, *Exceptional collections of line bundles on the Beauville surface*. arXiv.

A. Gorodentsev, S. Kuleshov, *Helix theory*, Mosc. Math. J. 4 (2004), no. 2, 377--440. journal

S. Kuleshov and D. Orlov, *Exceptional sheaves on Del Pezzo surfaces*, Russian Acad. Sci. Izv. Math. 44 (1995), no. 3, 479--513. journal.

C. Ingalls and A. Kuznetsov, *On nodal Enriques surfaces and quartic double solids*. arXiv.

S. Mukai, *Duality between D(X) and D(X^) with its application to Picard sheaves*, Nagoya Math. J. 81 (1981), 153--175. journal.

A. Rudakov, *Markov numbers and exceptional bundles on P*^{2}, Math. USSR-Izv. 32 (1989), no. 1, 99--112. journal.

S. Zube, *Exceptional vector bundles on Enriques surfaces*, Math. Notes 61 (1997), no. 5--6, 693--699. arXiv.

Links to the seminar from previous years.

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