Mathematics – Algebraic Geometry
Scientific paper
2008-05-27
Bull. London Math. Soc. 2009
Mathematics
Algebraic Geometry
One typo corrected; final version accepted for publication in Bull. London Math. Soc
Scientific paper
10.1112/blms/bdp017
Let $X$ be an irreducible smooth projective curve of genus $g\ge3$ defined over the complex numbers and let ${\mathcal M}_\xi$ denote the moduli space of stable vector bundles on $X$ of rank $n$ and determinant $\xi$, where $\xi$ is a fixed line bundle of degree $d$. If $n$ and $d$ have a common divisor, there is no universal vector bundle on $X\times {\mathcal M}_\xi$. We prove that there is a projective bundle on $X\times {\mathcal M}_\xi$ with the property that its restriction to $X\times\{E\}$ is isomorphic to $P(E)$ for all $E\in\mathcal{M}_\xi$ and that this bundle (called the projective Poincar\'e bundle) is stable with respect to any polarization; moreover its restriction to $\{x\}\times\mathcal{M}_\xi$ is also stable for any $x\in X$. We prove also stability results for bundles induced from the projective Poincar\'e 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 $\mathcal{M}_\xi$ 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.
Biswas Indranil
Brambila-Paz Leticia
Newstead Peter E.
No associations
LandOfFree
Stability of projective Poincare and Picard bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stability of projective Poincare and Picard bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability of projective Poincare and Picard bundles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-273860