We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces.
@article{bwmeta1.element.doi-10_2478_s11533-012-0008-8, author = {Matei Toma}, title = {Vector bundles on blown-up Hopf surfaces}, journal = {Open Mathematics}, volume = {10}, year = {2012}, pages = {1356-1360}, zbl = {1272.32015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0008-8} }
Matei Toma. Vector bundles on blown-up Hopf surfaces. Open Mathematics, Tome 10 (2012) pp. 1356-1360. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0008-8/
[1] Buchdahl N.P., Blowups and gauge fields, Pacific J. Math., 2000, 196(1), 69–111 http://dx.doi.org/10.2140/pjm.2000.196.69 | Zbl 1073.32506
[2] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, Aspects Math., E31, Friedrich Vieweg & Sohn, Braunschweig, 1997 | Zbl 0872.14002
[3] Lübke M., Teleman A., The Kobayashi-Hitchin Correspondence, World Scientific, River Edge, 1995 http://dx.doi.org/10.1142/2660 | Zbl 0849.32020
[4] Plantiko R., A rigidity property of class VII0 surface fundamental groups, J. Reine Angew. Math., 1995, 465, 145–163
[5] Schöbel K., Moduli spaces of PU(2)-instantons on minimal class VII surfaces with b 2 = 1, Ann. Inst. Fourier (Grenoble), 2008, 58(5), 1691–1722 http://dx.doi.org/10.5802/aif.2395 | Zbl 1159.14022
[6] Teleman A., Donaldson theory on non-Kählerian surfaces and class VII surfaces with b 2 = 1, Invent. Math., 2005, 162(3), 493–521 http://dx.doi.org/10.1007/s00222-005-0451-2 | Zbl 1093.32006
[7] Teleman A., The pseudo-effective cone of a non-Kählerian surface and applications, Math. Ann., 2006, 335(4), 965–989 http://dx.doi.org/10.1007/s00208-006-0782-3 | Zbl 1096.32011
[8] Teleman A., Instantons and curves on class VII surfaces, Ann. of Math., 2010, 172(3), 1749–1804 http://dx.doi.org/10.4007/annals.2010.172.1749 | Zbl 1231.14028
[9] Toma M., Compact moduli spaces of stable sheaves over non-algebraic surfaces, Doc. Math., 2001, 6, 9–27 | Zbl 0973.32007