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Stable real algebraic vector bundles over a Klein bottle
Author(s):
Usha
N.
Bhosle;
Indranil
Biswas
Journal:
Trans. Amer. Math. Soc.
360
(2008),
4569-4595.
MSC (2000):
Primary 14H60;
Secondary 14P99
Posted:
April 10, 2008
MathSciNet review:
2403697
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Abstract:
Let  be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that  does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over  .
References:
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- [AG]
- Norman L. Alling and Newcomb Greenleaf, Foundations of the theory of Klein surfaces, Lecture Notes in Mathematics, Vol. 219, Springer-Verlag, Berlin-New York, 1971. MR 0333163 (48:11488)
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- Michael F. Atiyah, Vector bundles over an elliptic curve, Proc. Lond. Math. Soc. 7 (1957), 414-452. MR 0131423 (24:A1274)
- [HL]
- Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31. Friedr. Vieweg & Sohn, Braunschweig, 1997. MR 1450870 (98g:14012)
- [Ne]
- Peter E. Newstead, Introduction to moduli problems and orbit spaces, T.I.F.R. Lectures on Mathematics and Physics, 51, Narosa Publishing House, New Delhi, 1978. MR 546290 (81k:14002)
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- Robert Silhol, Real algebraic surfaces, Lect. Notes Math. no. 1392, Springer-Verlag, Berlin Heidelberg, 1989 MR 1015720 (91i:14045)
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Additional Information:
Usha
N.
Bhosle
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Email:
usha@math.tifr.res.in
Indranil
Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Email:
indranil@math.tifr.res.in
DOI:
10.1090/S0002-9947-08-04564-9
PII:
S 0002-9947(08)04564-9
Keywords:
Stable bundle,
real algebraic curve,
Klein bottle
Received by editor(s):
February 26, 2006
Posted:
April 10, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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