We describe explicitly the moduli spaces of polystable holomorphic structures with on a rank two vector bundle with and for all minimal class VII surfaces with and with respect to all possible Gauduchon metrics . These surfaces are non-elliptic and non-Kähler complex surfaces and have recently been completely classified. When is a half or parabolic Inoue surface, is always a compact one-dimensional complex disc. When is an Enoki surface, one obtains a complex disc with finitely many transverse self-intersections whose number becomes arbitrarily large when varies in the space of Gauduchon metrics. can be identified with a moduli space of -instantons. The moduli spaces of simple bundles of the above type lead to interesting examples of non-Hausdorff singular one-dimensional complex spaces.
Nous décrirons explicitement les espaces de modules de structures holomorphes polystables avec sur un fibré vectoriel de rang deux avec et pour toutes les surfaces minimales de la classe VII avec et par rapport à toutes les métriques de Gauduchon . Ces surfaces sont des surfaces complexes non-elliptiques et non-Kählériennes et ont récemment été complètement classifiées. Si est une demi-surface d’Inoue ou une surface d’Inoue parabolique, est toujours un disque complexe compact de dimension un. Si est une surface d’Enoki, on obtient un disque complexe avec un nombre fini d’auto-intersections transverses, arbitrairement grand quand varie dans l’espace des métriques de Gauduchon. peut être identifié à un espace de modules de -instantons. Les espaces de modules de fibrés simples du type considéré mènent à des exemples intéressants d’espaces complexes singuliers non-Hausdorff de dimension un.
Keywords: Moduli spaces, holomorphic bundles, complex surfaces, instantons
Mot clés : espaces de modules, fibrés holomorphes, surfaces complexes, instantons
Schöbel, Konrad 1
@article{AIF_2008__58_5_1691_0, author = {Sch\"obel, Konrad}, title = {Moduli {Spaces} of ${\rm PU}(2)${-Instantons} on {Minimal} {Class~VII} {Surfaces} with $b_2=1$}, journal = {Annales de l'Institut Fourier}, pages = {1691--1722}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {5}, year = {2008}, doi = {10.5802/aif.2395}, mrnumber = {2445830}, zbl = {1159.14022}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2395/} }
TY - JOUR AU - Schöbel, Konrad TI - Moduli Spaces of ${\rm PU}(2)$-Instantons on Minimal Class VII Surfaces with $b_2=1$ JO - Annales de l'Institut Fourier PY - 2008 SP - 1691 EP - 1722 VL - 58 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2395/ DO - 10.5802/aif.2395 LA - en ID - AIF_2008__58_5_1691_0 ER -
%0 Journal Article %A Schöbel, Konrad %T Moduli Spaces of ${\rm PU}(2)$-Instantons on Minimal Class VII Surfaces with $b_2=1$ %J Annales de l'Institut Fourier %D 2008 %P 1691-1722 %V 58 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2395/ %R 10.5802/aif.2395 %G en %F AIF_2008__58_5_1691_0
Schöbel, Konrad. Moduli Spaces of ${\rm PU}(2)$-Instantons on Minimal Class VII Surfaces with $b_2=1$. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1691-1722. doi : 10.5802/aif.2395. https://aif.centre-mersenne.org/articles/10.5802/aif.2395/
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