Vector bundles on blown-up Hopf surfaces

• Autorzy: Matei Toma
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Compact complex surfaces; Moduli spaces; Hopf surfaces; Vector bundles

Kategorie tematyczne

• 32G13: Analytic moduli problems
• 32J15: Compact surfaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1356-1360

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Matei Toma

• Université Henri Poincaré, CNRS, INRIA

Bibliografia

• [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
• [2] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, Aspects Math., E31, Friedrich Vieweg & Sohn, Braunschweig, 1997
• [3] Lübke M., Teleman A., The Kobayashi-Hitchin Correspondence, World Scientific, River Edge, 1995 http://dx.doi.org/10.1142/2660
• [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
• [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
• [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
• [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
• [9] Toma M., Compact moduli spaces of stable sheaves over non-algebraic surfaces, Doc. Math., 2001, 6, 9–27

Identyfikatory

DOI

10.2478/s11533-012-0008-8