scholarly journals Totally geodesic subvarieties in the moduli space of curves

2020 ◽  
pp. 2050020
Author(s):  
Alessandro Ghigi ◽  
Gian Pietro Pirola ◽  
Sara Torelli
Keyword(s):  
Moduli Space ◽  
Abelian Varieties ◽  
Moduli Space Of Curves ◽  
Totally Geodesic

In this paper, we study totally geodesic subvarieties [Formula: see text] of the moduli space of principally polarized abelian varieties with respect to the Siegel metric, for [Formula: see text]. We prove that if [Formula: see text] is generically contained in the Torelli locus, then [Formula: see text].

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.

scholarly journals On the dimension of totally geodesic submanifolds in the Prym loci

2021 ◽  
Author(s):  
Elisabetta Colombo ◽  
Paola Frediani
Keyword(s):  
Moduli Space ◽  
Abelian Varieties ◽  
Double Cover ◽  
Totally Geodesic Submanifold ◽  
Totally Geodesic ◽  
Geodesic Submanifolds ◽  
Geodesic Submanifold ◽  
Totally Geodesic Submanifolds ◽  
Double Covers

AbstractIn this paper we give a bound on the dimension of a totally geodesic submanifold of the moduli space of polarised abelian varieties of a given dimension, which is contained in the Prym locus of a (possibly) ramified double cover. This improves the already known bounds. The idea is to adapt the techniques introduced by the authors in collaboration with A. Ghigi and G. P. Pirola for the Torelli map to the case of the Prym maps of (ramified) double covers.

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.

Sign in / Sign up

Export Citation Format

Share Document