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Exceptional orbits of the pure Mapping Class Group in the character variety.

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Title: Exceptional orbits of the pure Mapping Class Group in the character variety.
Authors: Golsefidy, Alireza S1 (AUTHOR), Tamam, Nattalie2 (AUTHOR)
Source: IMRN: International Mathematics Research Notices. Aug2026, Vol. 2026 Issue 15, p1-32. 32p.
Subject Terms: *Representations of groups (Algebra)
Abstract: Our primary objective is to construct closed subschemes of the character variety of the two-holed torus and the twisted character variety of a genus- |$2$| surface that satisfy the following properties: (1) They are invariant under the action of the corresponding pure Mapping Class Groups (MCGs). (2) They contain characters arising from dense representations into |$\operatorname{SU}_{2}(\mathbb{C})$| and |$\operatorname{SL}_{2}(\mathbb{Z}_{p})$| for primes |$p> 5$|⁠. (3) For any characteristic zero field |$F$|⁠ , and every absolutely irreducible character |$x$| in the |$F$| -points of these subschemes, the Zariski closure of the pure MCG orbit of |$x$| in the modified relative character variety has strictly smaller dimension. Our construction shows that [9, Theorem 1.4] is incorrect. In [5], we prove that these subschemes precisely characterize the locus of exceptional infinite orbits under the action of pure MCGs. [ABSTRACT FROM AUTHOR]
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  Data: Exceptional orbits of the pure Mapping Class Group in the character variety.
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  Data: <searchLink fieldCode="AR" term="%22Golsefidy%2C+Alireza+S%22">Golsefidy, Alireza S</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tamam%2C+Nattalie%22">Tamam, Nattalie</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22IMRN%3A+International+Mathematics+Research+Notices%22">IMRN: International Mathematics Research Notices</searchLink>. Aug2026, Vol. 2026 Issue 15, p1-32. 32p.
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  Data: Our primary objective is to construct closed subschemes of the character variety of the two-holed torus and the twisted character variety of a genus- |$2$| surface that satisfy the following properties: (1) They are invariant under the action of the corresponding pure Mapping Class Groups (MCGs). (2) They contain characters arising from dense representations into |$\operatorname{SU}_{2}(\mathbb{C})$| and |$\operatorname{SL}_{2}(\mathbb{Z}_{p})$| for primes |$p> 5$|⁠. (3) For any characteristic zero field |$F$|⁠ , and every absolutely irreducible character |$x$| in the |$F$| -points of these subschemes, the Zariski closure of the pure MCG orbit of |$x$| in the modified relative character variety has strictly smaller dimension. Our construction shows that [9, Theorem 1.4] is incorrect. In [5], we prove that these subschemes precisely characterize the locus of exceptional infinite orbits under the action of pure MCGs. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196059868
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        Value: 10.1093/imrn/rnag171
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        Text: English
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        PageCount: 32
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      – TitleFull: Exceptional orbits of the pure Mapping Class Group in the character variety.
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              Text: Aug2026
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              Y: 2026
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