Geodesic
Algebraic Nahm transform for parabolic Higgs bundles on ℙ1
Aker, Kürşat1 ; Szabó, Szilárd2
1 Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt, KKTC, 10 Mersin, Turkey
2 Department of Mathematics, Budapest University of Technology and Economics, Egry J. u. 1, H. ép., Budapest, 1111, Hungary
Geometry & topology, Tome 18 (2014) no. 5, pp. 2487-2545.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We formulate the Nahm transform in the context of parabolic Higgs bundles on ℙ1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles of arbitrary order and arbitrary behavior. Our methods are constructive in nature and examples are provided. The extended Nahm transform is established as an algebraic duality between moduli spaces of parabolic Higgs bundles. The guiding principle behind the construction is to investigate the behavior of spectral data near the poles of Higgs fields.

DOI : 10.2140/gt.2014.18.2487
Classification : 14H60, 14E05, 14J26
Keywords: parabolic Higgs bundle, integral transform, birational geometry, spectral sheaf

Aker, Kürşat 1 ; Szabó, Szilárd 2

1 Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt, KKTC, 10 Mersin, Turkey
2 Department of Mathematics, Budapest University of Technology and Economics, Egry J. u. 1, H. ép., Budapest, 1111, Hungary 
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Aker, Kürşat; Szabó, Szilárd. Algebraic Nahm transform for parabolic Higgs bundles on ℙ1. Geometry & topology, Tome 18 (2014) no. 5, pp. 2487-2545. doi : 10.2140/gt.2014.18.2487. http://geodesic.mathdoc.fr/articles/10.2140/gt.2014.18.2487/

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