Thin monodromy in Sp(4)
Algebraic Geometry
2019-02-20 v1 Number Theory
Abstract
We show that some hypergeometric monodromy groups in Sp(4,Z) split as free or amalgamated products and hence by cohomological considerations give examples of Zariski dense, non-arithmetic monodromy groups of real rank 2. In particular, we show that the monodromy of the natural quotient of the Dwork family of quintic threefolds in P^{4} splits as Z*Z/5. As a consequence, for a smooth quintic threefold X we show that a certain group of autoequivalences of the bounded derived category of coherent sheaves is an Artin group of dihedral type.
Cite
@article{arxiv.1210.0523,
title = {Thin monodromy in Sp(4)},
author = {Christopher Brav and Hugh Thomas},
journal= {arXiv preprint arXiv:1210.0523},
year = {2019}
}