Invariant hypercomplex structures and algebraic curves

We show that U(k)$U(k)$‐invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in gl(k,C)${\mathfrak {g} \mathfrak {l}}(k,{\mathbb {C}})$ correspond to algebraic curves C of genus (k−1)2$(k-1)^2$, equipped with a flat projection π:C→P1$\pi :C\rightarrow {\mathbb {P}...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 296; no. 1; pp. 122 - 129
Main Author Bielawski, Roger
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.01.2023
Subjects
adjoint orbits
Algebra
algebraic curves
Hilbert schemes of morphisms
hypercomplex structures
Invariants
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Summary:We show that U(k)$U(k)$‐invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in gl(k,C)${\mathfrak {g} \mathfrak {l}}(k,{\mathbb {C}})$ correspond to algebraic curves C of genus (k−1)2$(k-1)^2$, equipped with a flat projection π:C→P1$\pi :C\rightarrow {\mathbb {P}}^1$ of degree k, and an antiholomorphic involution σ:C→C$\sigma :C\rightarrow C$ covering the antipodal map on P1${\mathbb {P}}^1$.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202100223