38th Autumn School in Algebraic Geometry

Cox Rings and Mori Dream Spaces

Lukecin, Poland, September 6 - September 12, 2015

Teachers: Juergen Hausen (Tuebingen) and Antonio Laface (Concepcion) with collaboration of Simon Keicher (Tuebingen)

Summary: The Cox ring of an algebraic variety naturally generalizes the homogeneous coordinate ring of the projective space. Projective varieties with finitely generated Cox ring are called Mori dream spaces. In this setting, the Cox ring is a powerful tool for the explicit study of the underlying variety.
After introducing Cox rings and presenting basic algebraic and geometric aspects, the school continues with the following topics: relations to toric geometry, finite generation, varieties with higher complexity torus actions, the surface case and computational aspects of Cox rings and Mori dream spaces.
The prerequisites are basic algebraic geometry, also some knowledge on toric geometry will be helpful. A basic reference is the book Cox Rings by Arzhantsev, Derenthal, Hausen and Laface (Cambridge University Press).

Program of the school: Two lectures each morning, 90 min each, followed by two 60 min excercise sessions in the afternoon.

Notes to talks by Simon Keicher: part I, part II.

Organizers: Joachim Jelisiejew, Lukasz Sienkiewicz, Jaroslaw Wisniewski, Institute of Mathematics, the University of Warsaw.

The school is supported by: Warsaw Center of Mathematics and Computer Science, Institute of Mathematics of the University of Warsaw and by research projects Algebraic geometry: varieties and structure (2013/08/A/ST1/00804) and Algebraic varieties: arithmetic and geometry (2012/07/B/ST1/03343) grant of Polish Center of Scientific Research.

Conference picture, more pictures here.

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