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On the Geometry of the Moduli Space of Real Binary Octics


Published:20110430
Printed: Aug 2011
Kenneth C. K. Chu,
Department of Mathematics, University of Utah, Salt Lake City, Utah, USA
Abstract
The moduli space of smooth real binary octics has five connected
components. They parametrize the real binary octics whose defining
equations have $0,\dots,4$ complexconjugate 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
realanalytic manifold to the quotient of an open dense subset of
$5$dimensional real hyperbolic space $\mathbb{RH}^5$ by the action of an
arithmetic subgroup of $\operatorname{Isom}(\mathbb{RH}^5)$. These subgroups are
commensurable to discrete hyperbolic reflection groups, and the
Vinberg diagrams of the latter are computed.
MSC Classifications: 
32G13, 32G20, 14D05, 14D20 show english descriptions
Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] Structure of families (PicardLefschetz, monodromy, etc.) Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
32G13  Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 32G20  Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] 14D05  Structure of families (PicardLefschetz, monodromy, etc.) 14D20  Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
