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STABILITY OF THE PICARD BUNDLE

Published online by Cambridge University Press:  24 March 2003

I. BISWAS ,
L. BRAMBILA-PAZ ,
T. L. GÓMEZ  and
P. E. NEWSTEAD
I. BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, Indiaindranil@math.tifr.res.in
L. BRAMBILA-PAZ
Affiliation:
CIMAT, Apdo. Postal 402, C.P. 36240, Guanajuato, Méxicolebp@cimat.mx
T. L. GÓMEZ
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India tomas@math.tifr.res.in
P. E. NEWSTEAD
Affiliation:
Dept. of Mathematical Sciences, The University of Liverpool, Peach St., Liverpool L69 7ZL newstead@liv.ac.uk
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Abstract

Let $X$ be a non-singular algebraic curve of genus $g\ge 2,\;n\ge 2$ an integer, $\xi$ a line bundle over $X$ of degree $d>2n(g-1)$ with $(n,d)=1$ and ${\cal M}_\xi$ the moduli space of stable bundles of rank $n$ and determinant $\xi$ over $X$ . It is proved that the Picard bundle ${\cal W}_\xi$ is stable with respect to the unique polarisation of ${\cal M}_\xi$ .

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 5 , September 2002 , pp. 561 - 568
Copyright
© The London Mathematical Society 2002

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Footnotes

All the authors are members of the research group VBAC (Vector Bundles on Algebraic Curves), which is partially supported by EAGER (EC FP5 Contract no. HPRN-CT-2000-00099) and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101). The second author acknowledges support from CONA-CYT grant no. 28492-E. The third author was supported by a postdoctoral fellowship of the Ministerio de Educación y Cultura (Spain).