Boundary of the Gothen components

Abstract

In this short note we describe an interesting new phenomenon about the $\mathrm{Sp}(4,\mathbb{R})$-character variety. Precisely, we show that the Hitchin component and all Gothen components share the same boundary in our length spectrum compactification.

arXiv comment13 pages, comments welcome. arXiv admin note: text overlap with arXiv:2010.03499

References in corpus (7)

• Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
• Higgs bundles and surface group representations in the real symplectic group
• Deformations of maximal representations in Sp(4,R)
• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• Planar minimal surfaces with polynomial growth in the $\mathrm{Sp}(4,\mathbb{R})$-symmetric space
• Limits of Blaschke metrics
• Length spectrum compactification of the ${\mathrm{SO}}_0(2,3)$-Hitchin component