Stability of symplectic and orthogonal Poincaré bundles

Let L be a line bundle on a smooth complex projective curve X. Let ML be the moduli space of regularly stable orthogonal or symplectic bundles of rank r on X with fixed determinant L. There is a Poincaré projective bundle on X×ML. It defines a principal PSp(r,C) (respectively, PS0(r,C)) bundle P on...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 76; pp. 97 - 106
Main Authors Biswas, Indranil, Gómez, Tomás L.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2014
Subjects
Poincaré bundle
Stability
Symplectic and orthogonal bundle
Symplectic and orthogonal bundle
14F05
Stability
14D20
Poincaré bundle
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Summary:Let L be a line bundle on a smooth complex projective curve X. Let ML be the moduli space of regularly stable orthogonal or symplectic bundles of rank r on X with fixed determinant L. There is a Poincaré projective bundle on X×ML. It defines a principal PSp(r,C) (respectively, PS0(r,C)) bundle P on X×ML in the symplectic (respectively, orthogonal) case. For a fixed point x on X, let Px be its restriction to {x}×ML. We prove that the principal bundle Px is stable. As a corollary, P is stable with respect to any polarization on X×ML.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2013.10.014