Special Lagrangian submanifolds and Algebraic complexity one Torus Actions

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dc.creatorGoldstein, Edward
dc.date2000-03-30
dc.date2000-04-19
dc.date.accessioned2026-07-07T04:34:33Z
dc.date.available2026-07-07T04:34:33Z
dc.descriptionIn 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 $σ$ of the canonical bundle of M. Any such $σ$ 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 $σ$ is an inverse of a holomorphic section $η$ 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 $η_j$ near $η$ 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).
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0003220
dc.identifierhttp://arxiv.org/abs/math/0003220
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58945
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subject53XX; 14XX
dc.titleSpecial Lagrangian submanifolds and Algebraic complexity one Torus Actions
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