Pragmatic 2013

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Scientific activities


All the topics and the open problems were related to “Higher Dimensional Algebraic Geometry". During the courses the teachers introduced all basic facts on the Minimal Model Program to generalize the classification of complex projective surfaces to higher dimensional. Moreover, using the Laurent polynomial f, they constructed the Picard--Fuchs differential operator L_f. Certain facts about the quantum cohomology of a Fano manifold X, introduced the regularised quantum differential operator Q_X. During the period were addressed more than 10 open problems which were attached by the participants divided in several groups.

Here is the schedule of the seminars and individual meetings during the period of the school.


  1. Introduction to the Minimal Model Program

  2. Minimal Model Program with scaling

  3. Existence of Minimal Models

  4. Existence of Mori Fiber spaces

  5. Termination of flips 

  6. Fedder's criterion

  7. Minimal Model Program in positive characteristic

  8. Sarkisov Program

Shokurov's Log Geography

Boundedness in birational geometry



Calendars of seminars


September 16 2013

  1. Introduction to the Minimal Model Program (Paolo Cascini)

  2. The Fano/Landau Ginzburg correspondence (Alessio Corti)



September 17 2013

  1. Minimal Model Program with scaling (Paolo Cascini)

  2. Laurent polynomials and their classical periods (Alessio Corti)



September 18 2013

  1. Existence of Minimal Models (Paolo Cascini)

  2. On the classification of Fano lattice polygons under mutations (Alessio Corti)



September 19 2013

  1. Existence of Mori Fiber spaces (Paolo Cascini)

  2. Toric MMP and SOD (Yujiro Kawamata)




September 20 2013

  1. Termination of flips (Paolo Cascini)

Individual meetings



September 23 2013

  1. Minimal Model Program in positive characteristic (Paolo Cascini)

  2. Some conjectures on the classification of orbifold del Pezzo surfaces (Alessio Corti)

Individual meetings


September 24 2013

  1. Sarkisov Program (Paolo Cascini)

  2. The Chen-Ruan cohomology of orbifolds (Alessio Corti)

Individual meetings


September 25 2013

  1. Fedder criterion (Paolo Cascini)

  2. The quantum cohomology of orbifolds (Alessio Corti)

Individual meetings



September 26 2013

  1. Shokurov’s Log Geography (Paolo Cascini)

  2. Derived categories of weighted projective space (Yujiro Kawamata)


September 27 2013

  1. Boundededness in birational geometry (Paolo Cascini)

  2. Smooth Delighe-Mumford toric stacks as geometric invariant theory quotients (Alessio Corti)

Individual meetings



September 30 2013

  1. The quantum orbifold cohomology of smooth Deligne-Mumford Fano toric stacks

(Alessio Corti)

Individual meetings



October 1 2013

  1. The quantum Lefschetz theorem for stacks (Alessio Corti)

Individual meetings



October 2 2013

  1. The monodromy at infinity of hypersurfaces in tori (Alessio Corti)

Individual meetings



October 3 2013

Presentations of the open problems by the participants


October 4 2013

Presentations of the open problems by the participants