CrossRef Open Access 2014 24 sitasi

Thin monodromy in Sp(4)

Christopher Brav Hugh Thomas

Abstrak

Abstract We show that some hypergeometric monodromy groups in ${\rm Sp}(4,\mathbf{Z})$ 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 group of the natural quotient of the Dwork family of quintic threefolds in $\mathbf{P}^{4}$ splits as $\mathbf{Z}\ast \mathbf{Z}/5\mathbf{Z}$ . As a consequence, for a smooth quintic threefold $X$ we show that the group of autoequivalences $D^{b}(X)$ generated by the spherical twist along ${\mathcal{O}}_{X}$ and by tensoring with ${\mathcal{O}}_{X}(1)$ is an Artin group of dihedral type.

Penulis (2)

Christopher Brav

Hugh Thomas

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Brav, C., Thomas, H. (2014). Thin monodromy in Sp(4). https://doi.org/10.1112/s0010437x13007550

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Informasi Jurnal

Tahun Terbit: 2014
Bahasa: en
Total Sitasi: 24×
Sumber Database: CrossRef
DOI: 10.1112/s0010437x13007550
Akses: Open Access ✓