scholarly journals Errata: On the fields of rationality for curves and for their Jacobian varieties (Nagoya Math. J., Vol. 88 (1982), 197–212)

1986 ◽  
Vol 103 ◽  
pp. 163-163
Author(s):  
Tsutomu Sekiguchi
Keyword(s):  
Nagoya Math ◽  
Jacobian Varieties

Jacobian Varieties

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

scholarly journals Abelian varieties attached to cycles of intermediate dimension

1979 ◽  
Vol 75 ◽  
pp. 95-119 ◽  
Author(s):  
Hiroshi Saito
Keyword(s):  
Abelian Variety ◽  
Projective Variety ◽  
Classical Case ◽  
Degree Zero ◽  
Algebraic Construction ◽  
Jacobian Varieties ◽  
Codimension One ◽  
Picard Variety ◽  
Complex Tori ◽  
Intermediate Jacobian

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.”

scholarly journals Correction to “Isospectral surfaces of small genus,” (Nagoya Math. J. Vol. 107 (1987), 13-24)

1990 ◽  
Vol 117 ◽  
pp. 227-227 ◽  
Author(s):  
Robert Brooks ◽  
Richard Tse
Keyword(s):  
Fundamental Domain ◽  
Nagoya Math ◽  
Small Genus

It was brought to our attention by Zoran Luicic and Milica Stojanovic, via Peter Gilkey, that some of the diagrams in our paper are not correct.The particular problems are the gluing diagrams for the pair of isospectral surfaces of genus 4, which occur on page 20. It is easy to check that the gluing diagrams given there give rise to a surface of the wrong genus. The problem arose because of carelessness in some of the identifications of some of the edges of the fundamental domain.

scholarly journals On the fields of rationality for curves and for their jacobian varieties

1982 ◽  
Vol 88 ◽  
pp. 197-212 ◽  
Author(s):  
Tsutomu Sekiguchi
Keyword(s):  
Hyperelliptic Curve ◽  
Partial Result ◽  
Jacobian Variety ◽  
Noetherian Scheme ◽  
Jacobian Varieties ◽  
Field Of Moduli ◽  
The One

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].

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