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.

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

References in corpus (2)

• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• Length spectrum compactification of the ${\mathrm{SO}}_0(2,3)$-Hitchin component