TY - JOUR

T1 - Real abelian varieties with many line bundles

AU - Joglar-Prieto, Nuria

AU - Kollár, János

N1 - Funding Information:
If n − m > 2, then let N M be an (n − 1) (n − 1) psubmatrix. Either its determinant is zero, or N is invertible. In the latter case, N = md (rational matrix), and we have a unique choice for d. We claim that the same d works for every N. Indeed, two (n − 1) (n − 1) submatrices N and N0 have an (n − 2) (n − 2) submatrix in commonpwhich cannot be identically zero for n − 1 > 3 since N and N0 are invertible. Thus ( m d)−1M is a matrix where all the (n − 1) (n − 1) submatrices have a rational determinant. 2 Acknowledgements. We thank J. Bochnak and W. Kucharz for several very helpful discussions and comments. The rst author was supported by a Marie Curie Postdoctoral Fellowship (number HPMF-CT-1999-00019) at the Department of Mathematics at the Vrije Universiteit, Amsterdam. Partial nancial support for the second author was provided by the NSF, under grant number DMS-0096268.

PY - 2003/1

Y1 - 2003/1

N2 - Let X and Y be affine nonsingular real algebraic varieties. A general problem in real algebraic geometry is to try to decide when a continuous map f : X → Y can be approximated by regular maps in the space of script c sign0 mappings from X to Y, equipped with the script c sign0 topology. This paper solves this problem when X is the connected component containing the origin of the real part of a complex Abelian variety and Y is the standard 2-dimensional sphere.

AB - Let X and Y be affine nonsingular real algebraic varieties. A general problem in real algebraic geometry is to try to decide when a continuous map f : X → Y can be approximated by regular maps in the space of script c sign0 mappings from X to Y, equipped with the script c sign0 topology. This paper solves this problem when X is the connected component containing the origin of the real part of a complex Abelian variety and Y is the standard 2-dimensional sphere.

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U2 - 10.1112/S0024609302001509

DO - 10.1112/S0024609302001509

M3 - Article

AN - SCOPUS:0037258992

SN - 0024-6093

VL - 35

SP - 79

EP - 84

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -