Hyperplane arrangements of Torelli type

Daniele Faenzi (1) , Daniel Matei , Jean Vallès (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 UPPA - Université de Pau et des Pays de l'Adour

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.

Domaines: Géométrie algébrique [math.AG]

Daniele Faenzi, Daniel Matei, Jean Vallès. Hyperplane arrangements of Torelli type. Compositio Mathematica, 2013. ⟨hal-01993895⟩