Boundary of the Gothen components
Charles Ouyang, Andrea Tamburelli
TL;DR
This paper reveals that the Hitchin component and all Gothen components of the $ ext{Sp}(4, ext{R})$-character variety share the same boundary in the length spectrum compactification, highlighting a new geometric phenomenon.
Contribution
It demonstrates that these components have identical boundaries in the length spectrum compactification, a novel insight into their geometric structure.
Findings
Hitchin and Gothen components share the same boundary
Length spectrum compactification applies to these components
New geometric phenomenon identified in character varieties
Abstract
In this short note we describe an interesting new phenomenon about the -character variety. Precisely, we show that the Hitchin component and all Gothen components share the same boundary in our length spectrum compactification.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology