Asymptotic behaviour and the moduli space of doubly-periodic instantons
Journal of the European Mathematical Society, Tome 3 (2001) no. 4, pp. 335-375
Cet article a éte moissonné depuis la source EMS Press
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line 3, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to T2À1. The converse statement is also true, namely a holomorphic bundle on T2À1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally, we study the hyperkähler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously defined by the second author is a hyperkähler isometry with the moduli space of certain meromorphic Higgs bundles on the dual torus.
@article{JEMS_2001_3_4_a1,
author = {Olivier Biquard and Marcos Jardim},
title = {Asymptotic behaviour and the moduli space of doubly-periodic instantons},
journal = {Journal of the European Mathematical Society},
pages = {335--375},
year = {2001},
volume = {3},
number = {4},
doi = {10.1007/s100970100032},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970100032/}
}
TY - JOUR AU - Olivier Biquard AU - Marcos Jardim TI - Asymptotic behaviour and the moduli space of doubly-periodic instantons JO - Journal of the European Mathematical Society PY - 2001 SP - 335 EP - 375 VL - 3 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.1007/s100970100032/ DO - 10.1007/s100970100032 ID - JEMS_2001_3_4_a1 ER -
%0 Journal Article %A Olivier Biquard %A Marcos Jardim %T Asymptotic behaviour and the moduli space of doubly-periodic instantons %J Journal of the European Mathematical Society %D 2001 %P 335-375 %V 3 %N 4 %U http://geodesic.mathdoc.fr/articles/10.1007/s100970100032/ %R 10.1007/s100970100032 %F JEMS_2001_3_4_a1
Olivier Biquard; Marcos Jardim. Asymptotic behaviour and the moduli space of doubly-periodic instantons. Journal of the European Mathematical Society, Tome 3 (2001) no. 4, pp. 335-375. doi: 10.1007/s100970100032
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