Mathematics – Differential Geometry
Scientific paper
2000-03-30
Mathematics
Differential Geometry
15 pages
Scientific paper
In the first part of this paper we consider compact algebraic manifolds M^2n with an algebraic (n-1)-Torus action. We show that there is a T-invariant meromorphic section $\sigma$ of the canonical bundle of M. Any such $\sigma$ defines a divisor D. On the complement M'=M-D we have a trivialization of the canonical bundle and a T-action. If the first cohomology of M' vanishes, then results of [2] imply that there is a Special Lagrangian (SLag) fibration on M'. We study how the fibers compactify in M and give examples of SLag fibrations on M', including some cases there the first cohomology of M' doesn't vanish. In the second part of the paper we study Calabi-Yau hypersurfaces in M. We assume that $\sigma$ is an inverse of a holomorphic section $\eta$ of the anti-canonical bundle of M. We will see that under certain assumptions one can choose a holomorphic volume form on the smooth part D' of the divisor D s.t. orbits of the T-action give a SLag fibration on D' with respect to the metric, induced from M. Transversal sections $\eta_j$ near $\eta$ define smooth Calabi-Yau hypersurfaces D_j in M. We will show that one can deform the SLag fibration on D' to SLag fibrations on large parts of D_j. This construction applies for instance for D_j being quintics in CP^4 or Calabi-Yau hypersurfaces in the Grassmanian G(2,4).
No associations
LandOfFree
Special Lagrangian submanifolds and Algebraic complexity one Torus Actions 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 Special Lagrangian submanifolds and Algebraic complexity one Torus Actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Special Lagrangian submanifolds and Algebraic complexity one Torus Actions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-201962