On the Theory of θ-Functions, the Moduli of Abelian Varieties, and the Moduli of Curves

1962 ◽  
Vol 75 (2) ◽  
pp. 342 ◽  
Author(s):  
Walter L. Baily
Keyword(s):  
Abelian Varieties ◽  
Moduli Of Curves

Tropical Geometric Compactification of Moduli, II: A g Case and Holomorphic Limits

2018 ◽  
Vol 2019 (21) ◽  
pp. 6614-6660 ◽  
Author(s):  
Yuji Odaka
Keyword(s):  
Algebraic Curves ◽  
Abelian Varieties ◽  
Moduli Of Curves ◽  
Complex Dimension ◽  
Crucial Difference ◽  
Flat Tori ◽  
Hausdorff Limits

Abstract We compactify the classical moduli variety Ag of principally polarized abelian varieties of complex dimension g, by attaching the moduli of flat tori of real dimensions at most g in an explicit manner. Equivalently, we explicitly determine the Gromov–Hausdorff limits of principally polarized abelian varieties. This work is analogous to [50], where we compactified the moduli of curves by attaching the moduli of metrized graphs. Then, we also explicitly specify the Gromov–Hausdorff limits along holomorphic families of abelian varieties and show that these form special nontrivial subsets of the whole boundary. We also do the same for algebraic curves case and observe a crucial difference with the case of abelian varieties.

Analytic Theory of Abelian Varieties

1974 ◽  
Author(s):  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Abelian Varieties ◽  
Analytic Theory

scholarly journals Classification of nonrigid families of abelian varieties

1993 ◽  
Vol 45 (2) ◽  
pp. 159-189
Author(s):  
Masa-Hiko Saitō
Keyword(s):  
Abelian Varieties

scholarly journals Some results about the projective normality of abelian varieties

2005 ◽  
Vol 85 (5) ◽  
pp. 409-418 ◽  
Author(s):  
Luis Fuentes García
Keyword(s):  
Abelian Varieties ◽  
Projective Normality

Very ample line bundles on quasi-abelian varieties

2001 ◽  
Vol 236 (1) ◽  
pp. 191-200 ◽  
Author(s):  
Shigeharu Takayama
Keyword(s):  
Abelian Varieties ◽  
Line Bundles
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