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Hyperplane arrangements of Torelli type

Part of: Discrete geometry (Co)homology theory Singularities Cycles and subschemes

Published online by Cambridge University Press:  14 December 2012

Daniele Faenzi ,
Daniel Matei  and
Jean Vallès
Daniele Faenzi
Affiliation:
Université de Pau et des Pays de l’Adour, Avenue de l’Université, BP 576, 64012 Pau cedex, France (email: daniele.faenzi@univ-pau.fr)
Daniel Matei
Affiliation:
Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, I.M.A.R., Bucharest, Romania, P.O. Box 1-764, RO-014700, Bucharest, Romania (email: Daniel.Matei@imar.ro)
Jean Vallès
Affiliation:
Université de Pau et des Pays de l’Adour, Avenue de l’Université, BP 576, 64012 Pau cedex, France (email: jean.valles@univ-pau.fr)
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Abstract

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We give a necessary and sufficient condition in order for a hyperplane arrangement to be of Torelli type, namely that it is recovered as the set of unstable hyperplanes of its Dolgachev sheaf of logarithmic differentials. Decompositions and semistability of non-Torelli arrangements are investigated.

Keywords

hyperplane arrangementsTorelli theoremunstable hyperplanessheaf of logarithmic differentials

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 14C34: Torelli problem 52C35: Arrangements of points, flats, hyperplanes 32S22: Relations with arrangements of hyperplanes
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 2 , February 2013 , pp. 309 - 332
Copyright
© The Author(s) 2012

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