Geometry Course

Infinitesimal Deformation Theory

Barbara Fantechi


This course will start in the week of nov 6 and will meet once a week until the end of january.
We will cover the basics of classical, infinitesimal deformation theory (see e.g. Schlessinger's theoem in Artin, Lecturs on deformations of singularities). We start by introducing the category of local artinian rings, introduce the notion of deformation functor, define prorepresentability and prorepresentable hulls; we will discuss the relationship with the cotangent complex for schemes and algebraic stacks. We will define tangent and obstruction spaces, and compute as many examples as possible. At the end of the course, if there is interest, we will have a seminar on differential graded algebras and extended deformation functors, and a shorter one on the notion of obstruction theory for an algebraic stack and the definition of virtual fundamental class.

Schedule: nov 6 - jan ? (oct 23 - 31 preliminary lectures)
Credits: 1

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