Mathematics – Algebraic Geometry
Scientific paper
1997-10-23
Mathematics
Algebraic Geometry
100 pages, LaTeX2e
Scientific paper
Let $M$ be a Kaehler manifold, and consider the total space $T^*M$ of the cotangent bundle to $M$. We show that in the formal neighborhood of the zero section $M \subset T^*M$ the space $T^*M$ admits a canonical hyperkaehler structure, compatible with the complex and holomorphic symplectic structures on $T^*M$. The associated hyperkaehler metric $h$ coincides with the given Kaehler metric on the zero section $M \subset T^*M$. Moreover, $h$ is invariant under the canonical circle action on $T^*M$ by dilatations along the fibers of $T^*M$ over $M$. We show that a hyperkaehler structure with these properties is unique. When the Kaehler metric on $M$ is real-analytic, we show that this formal hyperkaehler structure can be extended to an open neighborhood of the zero section. We also prove a hyperkaehler analog of the Darboux-Weinstein Theorem. To prove these results, we use the machinery of $R$-Hodge structures, following Deligne and Simpson.
No associations
LandOfFree
Hyperkaehler structures on total spaces of holomorphic cotangent 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 Hyperkaehler structures on total spaces of holomorphic cotangent bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperkaehler structures on total spaces of holomorphic cotangent bundles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-42644