Thin monodromy in Sp(4)

Christopher Brav, Hugh Thomas

Type: Article

Publication Date: 2014-03-01

Citations: 43

DOI: https://doi.org/10.1112/s0010437x13007550

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.

Locations

arXiv (Cornell University) - View - PDF
Archipelago (Université du Québec à Montréal) - View - PDF
DataCite API - View
Compositio Mathematica - View - PDF

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Action	Title	Year	Authors
+	Combinatorial Group Theory	1990	Roger C. Lyndon Paul E. Schupp
+	Monodromy calculatons of fourth order equations of Calabi-Yau type	2004	Christian van Enckevort Duco van Straten
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+ PDF Chat	Arithmeticity of certain symplectic hypergeometric groups	2014	Sandip Singh T. N. Venkataramana
+	Cohomology of Sp4(Z) and related groups and spaces	1985	Ronnie Lee Steven H. Weintraub
+	Groups of cohomological dimension one	1969	Richard G. Swan
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+	Derived autoequivalences and a weighted Beilinson resolution	2008	Alberto Canonaco Robert L. Karp