Reading seminar in algebraic geometry.
Fall 2022: Birational geometry and the minimal model program

This semester the reading seminar will study birational geometry.

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

1/28. Organizational meeting.

2/11 Paul Hacking. What is birational geometry?

2/18 Kristin DeVleming. Birational geometry in dimensions greater than 2.

2/25 No seminar due to weather.

3/4 Paul Hacking. Birational geometry: Examples in dimension 3.

3/11 Yuxuan Yang. Blowups.

3/18 Spring break

3/25 No seminar.

4/1 No seminar due to Geometry and Topology talk by Ailsa Keating

4/8 Chunlin Shao. ADE singularities and their generalizations.

4/15 Cristian Rodriguez. Terminal singularities of 3-folds.

4/22 Ethan Zhou. Finding rational curves via Mori's bend and break technique.

4/29 Joe Foster. Birational geometry of hyperkahler manifolds.




References

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

D. Huybrechts, Compact hyperkahler manifolds, in Calabi--Yau manifolds and related geometries, Springer, 2003.

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



Links to the seminar from previous semesters.

Fano varieties, Fall 2021
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