Hyperplane arrangements of Torelli type
Daniele Faenzi, Daniel Matei, Jean Vall\`es
TL;DR
This paper characterizes hyperplane arrangements of Torelli type through their Dolgachev sheaves, providing criteria for their identification and analyzing the properties of non-Torelli arrangements.
Contribution
It establishes a necessary and sufficient condition for Torelli type arrangements based on unstable hyperplanes of Dolgachev sheaves, advancing understanding of their structure.
Findings
Characterization of Torelli type arrangements via Dolgachev sheaves
Decomposition and semistability analysis of non-Torelli arrangements
Criteria for identifying arrangements of Torelli type
Abstract
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Mathematics and Applications · Finite Group Theory Research