scholarly journals The Structure of the Moduli Spaces of Curves and Abelian Varieties

2004 ◽  
pp. 37-45
Author(s):  
David Mumford
Keyword(s):  
Moduli Spaces ◽  
Abelian Varieties ◽  
Moduli Spaces Of Curves

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

2021 ◽  
Author(s):  
Anna Gori ◽  
Alberto Verjovsky ◽  
Fabio Vlacci
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
Complex Multiplication ◽  
Higher Dimension ◽  
Geometric Constructions ◽  
Flat Torus ◽  
Flat Tori

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

scholarly journals Moduli spaces of curves with homology chains and c = 1 matrix models

1994 ◽  
Vol 327 (3-4) ◽  
pp. 221-225 ◽  
Author(s):  
A.S. Cattaneo ◽  
A. Gamba ◽  
M. Martellini
Keyword(s):  
Matrix Models ◽  
Moduli Spaces ◽  
Moduli Spaces Of Curves
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