Skip to content
DraconiticResearch
Search Sources API
184,937 studies31 sourcesUpdated 59 min ago
PreprintarXiv licencearXiv

Character variety of the five-punctured sphere and the determinantal quintic hypersurface

  • Kazuhiro Hikami
Open at sourcePDFDOICite

Abstract

Using skein-theoretic methods, we study the SL2(C) character variety of the five-punctured sphere with arbitrary conjugacy class at each of the five punctures. We show that a Fricke-Klein-Vogt-type relation is realized as a symmetric determinantal hypersurface. We also give a realization of the character variety in terms of cluster variables. We explicitly derive the Poisson structure of the simple closed curves on the surface, and prove that cluster mutations induce automorphisms of the character variety.

Related

  1. The Chern character of a coherent sheaf on a smooth projective hypersurface
    David Favero, Tyler L. Kelly
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Punctured log Gromov-Witten theory of log modifications and double ramification cycles with target log variety
    Samuel Johnston
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. On symplectic aspects of SU(2) character varieties for punctured surfaces
    Aliakbar Daemi, Christopher Scaduto
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Untwisting the twisted character variety via a stacky curve
    Anna Borri
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Two-bridge knot epimorphisms and intersections in the character variety
    Isidora Bailly-Hall, Michelle Chu, Karina Dovgodko +3
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{hikami2026character,
  title = {{Character variety of the five-punctured sphere and the determinantal quintic hypersurface}},
  author = {Kazuhiro Hikami},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12092},
  eprint = {2610.12092},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12092},
}
RIS
TY  - UNPB
TI  - Character variety of the five-punctured sphere and the determinantal quintic hypersurface
AU  - Kazuhiro Hikami
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12092
UR  - https://arxiv.org/abs/2610.12092
AB  - Using skein-theoretic methods, we study the SL2(C) character variety of the five-punctured sphere with arbitrary conjugacy class at each of the five punctures. We show that a Fricke-Klein-Vogt-type relation is realized as a symmetric determinantal hypersurface. We also give a realization of the character variety in terms of cluster variables. We explicitly derive the Poisson structure of the simple closed curves on the surface, and prove that cluster mutations induce automorphisms of the character variety.
ER  -