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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Veröffentlicht in:	Mathematische Nachrichten 2023-01, Vol.296 (1), p.122-129
1. Verfasser:	Bielawski, Roger
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Sprache:	eng
Schlagworte:	adjoint orbits Algebra algebraic curves Hilbert schemes of morphisms hypercomplex structures Invariants
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description	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${\mathbb {P}}^1$.
doi_str_mv	10.1002/mana.202100223
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subjects	adjoint orbits Algebra algebraic curves Hilbert schemes of morphisms hypercomplex structures Invariants
title	Invariant hypercomplex structures and algebraic curves
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