On the Kodaira dimension of moduli spaces of abelian varieties with non-principal polarizations

2012 ◽  
Author(s):  
Yung-sheng Tai
Keyword(s):  
Moduli Spaces ◽  
Abelian Varieties ◽  
Kodaira Dimension

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.

Kummer Varieties and the Moduli Spaces of Abelian Varieties

1986 ◽  
Vol 108 (3) ◽  
pp. 615 ◽  
Author(s):  
Bert van Geemen ◽  
Gerard van der Geer
Keyword(s):  
Moduli Spaces ◽  
Abelian Varieties

TWO REMARKS ON SUBVARIETIES OF MODULI SPACES

2008 ◽  
Vol 19 (02) ◽  
pp. 237-243 ◽  
Author(s):  
KIRTI JOSHI
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Abelian Varieties ◽  
Moduli Space Of Curves ◽  
Rank Zero ◽  
Zero Locus

We study two natural questions about subvarieties of moduli spaces. In the first section, we study the locus of curves equipped with F-nilpotent bundles and its relationship to the p-rank zero locus of the moduli space of curves of genus g. In the second section, we study subvarieties of moduli spaces of vector bundles on curves. We prove an analogue of a result of F. Oort about proper subvarieties of moduli of abelian varieties.

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