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- W3129089076 abstract "Abstract Motivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in $${mathbb {R}}^{n}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:math> and investigate criteria to determine whether a n -dimensional flat torus has non trivial (i.e. bigger than $${mathbb {Z}}^{*}={mathbb {Z}}{setminus }{0}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mrow /><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo></mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mn>0</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math> ) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori." @default.
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- W3129089076 date "2021-02-08" @default.
- W3129089076 modified "2023-09-25" @default.
- W3129089076 title "A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication" @default.
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- W3129089076 doi "https://doi.org/10.1007/s00209-020-02679-2" @default.
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