Geometry Course
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**Infinitesimal Deformation Theory**

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Barbara Fantechi

**CONTENTS**

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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