Vector bundles on blown-up Hopf surfaces

Matei Toma

Open Mathematics (2012)

  • Volume: 10, Issue: 4, page 1356-1360
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Matei Toma. "Vector bundles on blown-up Hopf surfaces." Open Mathematics 10.4 (2012): 1356-1360. <http://eudml.org/doc/269623>.

@article{MateiToma2012,
abstract = {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.},
author = {Matei Toma},
journal = {Open Mathematics},
keywords = {Compact complex surfaces; Moduli spaces; Hopf surfaces; Vector bundles; compact complex surfaces; moduli spaces; vector bundles},
language = {eng},
number = {4},
pages = {1356-1360},
title = {Vector bundles on blown-up Hopf surfaces},
url = {http://eudml.org/doc/269623},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Matei Toma
TI - Vector bundles on blown-up Hopf surfaces
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1356
EP - 1360
AB - 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.
LA - eng
KW - Compact complex surfaces; Moduli spaces; Hopf surfaces; Vector bundles; compact complex surfaces; moduli spaces; vector bundles
UR - http://eudml.org/doc/269623
ER -

References

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  1. [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 Zbl1073.32506
  2. [2] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, Aspects Math., E31, Friedrich Vieweg & Sohn, Braunschweig, 1997 Zbl0872.14002
  3. [3] Lübke M., Teleman A., The Kobayashi-Hitchin Correspondence, World Scientific, River Edge, 1995 http://dx.doi.org/10.1142/2660 Zbl0849.32020
  4. [4] Plantiko R., A rigidity property of class VII0 surface fundamental groups, J. Reine Angew. Math., 1995, 465, 145–163 
  5. [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 Zbl1159.14022
  6. [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 Zbl1093.32006
  7. [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 Zbl1096.32011
  8. [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 Zbl1231.14028
  9. [9] Toma M., Compact moduli spaces of stable sheaves over non-algebraic surfaces, Doc. Math., 2001, 6, 9–27 Zbl0973.32007

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