Stability of projective Poincare and Picard bundles

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dc.creatorBiswas, I.
dc.creatorBrambila-Paz, L.
dc.creatorNewstead, P. E.
dc.date2008-05-27
dc.date2009-01-21
dc.date.accessioned2026-07-07T12:56:38Z
dc.date.available2026-07-07T12:56:38Z
dc.descriptionLet $X$ be an irreducible smooth projective curve of genus $g\ge3$ defined over the complex numbers and let ${\mathcal M}_ξ$ denote the moduli space of stable vector bundles on $X$ of rank $n$ and determinant $ξ$, where $ξ$ is a fixed line bundle of degree $d$. If $n$ and $d$ have a common divisor, there is no universal vector bundle on $X\times {\mathcal M}_ξ$. We prove that there is a projective bundle on $X\times {\mathcal M}_ξ$ with the property that its restriction to $X\times\{E\}$ is isomorphic to $P(E)$ for all $E\in\mathcal{M}_ξ$ and that this bundle (called the projective Poincaré bundle) is stable with respect to any polarization; moreover its restriction to $\{x\}\times\mathcal{M}_ξ$ is also stable for any $x\in X$. We prove also stability results for bundles induced from the projective Poincaré bundle by homomorphisms $\text{PGL}(n)\to H$ for any reductive $H$. We show further that there is a projective Picard bundle on a certain open subset $\mathcal{M}'$ of $\mathcal{M}_ξ$ for any $d>n(g-1)$ and that this bundle is also stable. We obtain new results on the stability of the Picard bundle even when $n$ and $d$ are coprime.
dc.descriptionOne typo corrected; final version accepted for publication in Bull. London Math. Soc
dc.identifierhttps://arxiv.org/abs/0805.4131
dc.identifierhttp://arxiv.org/abs/0805.4131
dc.identifierBull. London Math. Soc. 2009
dc.identifierdoi:10.1112/blms/bdp017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224649
dc.subjectAlgebraic Geometry
dc.subject14H60; 14J60
dc.titleStability of projective Poincare and Picard bundles
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