Motivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in ℝ and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than ℤ∗=ℤ∖{0}) 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.

A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication / A. Gori, F. Vlacci, A. Verjosky. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 299:1-2(2021 Oct), pp. 543-562. [10.1007/s00209-020-02679-2]

A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

A. Gori
;
2021

Abstract

Motivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in ℝ and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than ℤ∗=ℤ∖{0}) 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.
Flat tori; Conformal multiplication
Settore MAT/03 - Geometria
8-feb-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/869800
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