Author: David_Corfield Format: HtmlarXiv:0911.3845
Title: A short note on infinity-groupoids and the period map for projective manifolds
Authors: Domenico Fiorenza, Elena Martinengo
Abstract: A common criticism of infinity-categories in algebraic geometry is that they are an extremely technical subject, so abstract to be useless in everyday mathematics. The aim of this note, deliberately written in an informal style, is to show in a classical example that quite the converse is true: even a naive intuition of what an infinity-groupoid should be clarifies several aspects of the infinitesimal behaviour of the periods map of a projective manifold. In particular, the ad hoc constructions of arXiv:math/0605297v1 and subsequent works turn out to be completely natural from this perspective, and so classical results such as Griffiths' expression for the differential of the periods map, the so-called Kodaira principle on obstructions to deformations of projective manifolds, and the Bogomolov-Tian-Todorov theorem are easily recovered.
arXiv:0911.3845 Title: A short note on infinity-groupoids and the period map for projective manifolds Authors: Domenico Fiorenza, Elena Martinengo
Abstract: A common criticism of infinity-categories in algebraic geometry is that they are an extremely technical subject, so abstract to be useless in everyday mathematics. The aim of this note, deliberately written in an informal style, is to show in a classical example that quite the converse is true: even a naive intuition of what an infinity-groupoid should be clarifies several aspects of the infinitesimal behaviour of the periods map of a projective manifold. In particular, the ad hoc constructions of arXiv:math/0605297v1 and subsequent works turn out to be completely natural from this perspective, and so classical results such as Griffiths' expression for the differential of the periods map, the so-called Kodaira principle on obstructions to deformations of projective manifolds, and the Bogomolov-Tian-Todorov theorem are easily recovered.