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September 4-5, 2017 
University of Turin 


As a first approximation, one may think of an algebraic stack X as a variety (its coarse moduli space) by adding stabilisers along subvarieties. This holds for example in the case of toric stacks as defined by L. Borisov, L. Chen and G. Smith and by B. Fantechi, E. Mann and F. Nironi, and as studied by A. Geraschenko and M. Satriano.
At this workshop, two generalisations of this approach will be discussed. On the one hand, focusing on the group action, one can replace the torus action by the action of an arbitrary reductive group. This leads for instance to horospherical stacks as treated by A. Javanpeykar, K. Langlois and R. Terpereau
On the other hand, when thinking about toric varieties as the simplest class of Mori dream spaces (i.e. with its Cox ring being just a polynomial ring), one may arrive at Mori dream stacks as introduced by A. Hochenegger and E. Martinengo
Besides these two generalisations, some related topics will be presented.

Invited Speakers: 


The workshop will take place at the Department of Mathematics of the University of Turin on Monday September 4, in the afternoon, and on Tuesday September 5, 2017.

Monday, 4th:

  • 13.30 - 14.45: Ariyan Javanpeykar: Introduction to toric and horospherical stacks
  • 15.00 - 16.15: Kevin Langlois: Beyond horospherical stacks
  • 16.45 - 18:00: Andreas Hochenegger: Mori dream stacks
Tuesday, 5th:
  • 9.00-10.15: Ronan Terpereau: Invariant deformation theory of affine schemes equipped with reductive group action
  • 10.30-11.45: Fabio Tonini: Sheafification functors
  • 12.00-13.15: Daniel Bergh: Destackification and weak factorization of Deligne-Mumford stacks
  • 14.30: Discussions

For organisational reasons, please send a short email to: elena.martinengo@unito.it