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On the Geometry of the Moduli Space of Real Binary Octics

Published online by Cambridge University Press:  20 November 2018

Kenneth C. K. Chu
Kenneth C. K. Chu*
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah, USA e-mail: chu@math.utah.edu
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Abstract

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The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0, … , 4 complex-conjugate pairs of roots respectively. We show that each of these five components has a real hyperbolic structure in the sense that each is isomorphic as a real-analytic manifold to the quotient of an open dense subset of 5-dimensional real hyperbolic space $\mathbb{R}{{\mathbb{H}}^{5}}$ by the action of an arithmetic subgroup of Isom$\left( \mathbb{R}{{\mathbb{H}}^{5}} \right)$. These subgroups are commensurable to discrete hyperbolic reflection groups, and the Vinberg diagrams of the latter are computed.

Keywords

32G1332G2014D0514D20real binary octicsmoduli spacecomplex hyperbolic geometryVinberg algorithm
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 4 , 01 August 2011 , pp. 755 - 797
Copyright
Copyright © Canadian Mathematical Society 2011

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