SCHOOL (AND WORKSHOP) ON
THE GEOMETRY OF ALGEBRAIC
TRENTO, SEPTEMBER 1-6, 2008
B. Fantechi (SISSA, It) A. Kresch (Universität Zürich, CH)
Supporting lectures will be delivered by
General informations on the School and Workshop.
The School/Workshop is organized by G. Casnati, C. Fontanari, R. Notari, M.L. Spreafico. For contacting the organizers please send an e-mail to
The School/Workshop is supported by CIRM -Fondazione Bruno Kessler
(formerly CIRM-ITC), by GNSAGA-INdAM and by Dipartimento di
Matematica-Politecnico di Torino and Dipartimento di
Matematica-Università di Torino as part of the joint Project
"Geometria delle Varietà Algebriche e dei loro Spazi di Moduli"
cofinanced by Italian MIUR.
The School and the Workshop will take place at
Aim of the School.
The School is mainly aimed to Phd students and young researchers in Algebraic Geometry, introducing the participants to research, beginning from a basic level with a view towards the applications and to the most recent results.
A tentative program is as follows.
Motivation: why stacks are needed. Basic example: moduli of curves of genus g. The 2-category of groupoids, schemes as functors, categories fibered in groupoids, pseudofunctors. The stack condition. Representable morphisms, definition of algebraic stack (in the sense of Deligne-Mumford). Quotient stacks, stacks associated to groupoids. The 2-category of stacks; open, closed substacks; topological space associated to a stack. Properties of stacks and of their morphisms; valuative criteria for separatedness and properness. Inertia stack. (Quasi)coherent sheaves on a stack, cohomology of sheaves. Main worked out examples: moduli of stable pointed curves, moduli of stable sheaves, weighted projective stacks and toric DM stacks. Infinitesimal study of moduli stacks and deformation theory. A short introduction to Artin stacks will also be provided.
Aim of Workshop.
The Workshop is intended to discuss the state of the art in stacks and moduli theory. Up to now the following speakers have confirmed their participation: F. Catanese, G. Farkas, E. Sernesi, A. Verra, A. Vistoli. People interested in delivering a short communication are kindly requested to submit the title and an abstract within August 17th to
The School will start on Monday, 1st at 9.30 and it will end on Friday, 5th at 12.30. Workshop will start on Friday 5th at 14.30 and it will end on Saturday 6th at 14.00. On Friday evening a social dinner open to the participants of the School/Workshop will be organized.
Participants who do not require financial support are expected to fill in the on line registration form before August, 17th.