Reading seminar in algebraic geometry.
Fall 2021: Fano varieties

This semester the reading seminar will study Fano varieties.

The seminar will consist of 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, 2:30PM--3:30PM, in LGRT 1234.



Tentative Schedule

9/3. Organizational meeting.

9/17. Paul Hacking. What is a Fano variety?

9/24. Kristin DeVleming. K stability.

10/15 Ethan Zhou. del Pezzo surfaces.

10/22 No seminar.

10/29 Eyal Markman. TBA.

11/5 No seminar.

11/12 Yuxuan Yang. Cubic 3-folds following Clemens-Griffiths.

11/19 Joe Foster. Cubic 4-folds following Hassett.

11/26 No seminar (Thanksgiving).

12/3 Arthur Wang. The Fano variety as a hyperkahler 4-fold.

12/10 Cristian Rodriguez. Q Fano 3-folds.



References

J. Kollar and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math. 134, C.U.P., 1998.

A. Beauville, Complex algebraic surfaces, London Math. Soc. Stud. Texts 34, C.U.P., 1996.

P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, 1978.

C. Xu, K-stability of Fano varieties: an algebro-geometric approach, pdf, 2020.

S. Donaldson, Stability of algebraic varieties and Kahler geometry, pdf, 2018.

K. DeVleming, Notes on K-stability, pdf, 2019.

H. Clemens and P. Griffiths, The intermediate Jacobian of the cubic 3-fold, Annals of Math. 95, No. 2, 1972, pdf.

B. Hassett, Special cubic 4-folds, Harvard PhD thesis, 1996, pdf.

S. Altinok, G. Brown, and M. Reid, Fano 3-folds, K3 surfaces, and graded rings, arXiv.



Links to the seminar from previous semesters.

Mirror symmetry, Spring 2020
K3 surfaces, Fall 2019
The minimal model program, Spring 2019
Non-commutative K3 surfaces, Fall 2018
Topics in algebraic geometry, Spring 2018
Surface singularities, Fall 2017
Birational geometry, Spring 2017.
Algebraic surfaces, Fall 2016.
Fano varieties, Fall 2015
The Hitchin system, character varieties, and related topics, Spring 2015
Holomorphic symplectic varieties and Hyperkahler manifolds, Fall 2014
Syzygies, Spring 2014
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


This page is maintained by Paul Hacking hacking@math.umass.edu