Some Jacobian varieties which split

Author(s):  
Clifford J. Earle
Keyword(s):  
1986 ◽  
pp. 167-212 ◽  
Author(s):  
J. S. Milne
Keyword(s):  

1979 ◽  
Vol 75 ◽  
pp. 95-119 ◽  
Author(s):  
Hiroshi Saito

The group of cycles of codimension one algebraically equivalent to zero of a nonsingular projective variety modulo rational equivalence forms an abelian variety, i.e., the Picard variety. To the group of cycles of dimension zero and of degree zero, there corresponds an abelian variety, the Albanese variety. Similarly, Weil, Lieberman and Griffiths have attached complex tori to the cycles of intermediate dimension in the classical case. The aim of this article is to give a purely algebraic construction of such “intermediate Jacobian varieties.”


1982 ◽  
Vol 88 ◽  
pp. 197-212 ◽  
Author(s):  
Tsutomu Sekiguchi

Throughout the paper, a scheme means a noetherian scheme. By a curve C over a scheme S of genus g, we mean a proper and smooth S-scheme with irreducible curves of genus g as geometric fibres. In the previous paper [15], the author showed that the field of moduli for a non-hyperelliptic curve over a field coincides with the one for its canonically polarized jacobian variety, and in [16], he gave a partial result on the coincidence of the fields of rationality for a hyperelliptic curve and for its canonically polarized jacobian variety. In the present paper, we will discuss the isomorphy of the isomorphism schemes of two curves over a scheme and of their canonically polarized jacobian schemes, by using Oort-Steenbrink’s result [12].


1954 ◽  
Vol 59 (3) ◽  
pp. 505 ◽  
Author(s):  
Maxwell Rosenlicht

1960 ◽  
Vol 71 (2) ◽  
pp. 303 ◽  
Author(s):  
Walter L. Baily
Keyword(s):  

2015 ◽  
Vol 18 (1) ◽  
pp. 555-577 ◽  
Author(s):  
Jean-Marc Couveignes ◽  
Tony Ezome

We show how to efficiently evaluate functions on Jacobian varieties and their quotients. We deduce an algorithm to compute$(l,l)$isogenies between Jacobians of genus two curves in quasi-linear time in the degree$l^{2}$.


1999 ◽  
Vol 121 (1) ◽  
pp. 65-72
Author(s):  
Tomohide Terasoma ◽  
T. Shioda
Keyword(s):  

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