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
The School/Workshop is organized by G. Casnati, C. Fontanari, R. Notari, M.L. Spreafico. For contacting the organizers send a mail to
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.
A more detailed second announcement (containing informations on accomodation, registration and financial supports) will follow probably in February 2008.