Differential Geometry and Topology

course: Homogeneous toric bundles with positive first Chern class

speaker: Fabio Podestà (Università di Firenze)

abstract: We recall that a toric bundle is a bundle having a Kaehler toric manifold F as fiber and a subgroup of the torus Tn acting on F as structural group Ma. We consider the class of homogeneous toric bundles over a flag manifold GCP and we provide a simple algebraic criterion which characterizes the Fano manifolds in this class. Any such homogeneous toric bundle is almost GC-homogeneous HS and of G-cohomogeneity equal to n. These manifolds represent a natural generalization of the examples of cohomogeneity one manifolds, considered e.g. in DW,KS,PS,TZ.

DW A. Dancer and M. Wang: Kaehler-Einstein metrics of cohomogeneity one and bundle constructions for Einstein Hermitian metrics, Math. Ann. 312 (1998), 503-526

HS A. Huckleberry and D. Snow: Almost-homogeneous Kaehler manifolds with hypersurface orbits, Osaka J. Math. 19 (1982), 763-786

KS N. Koiso and Y. Sakane: Non-homogeneous Kaehler-Einstein manifolds on compact complex manifolds, in Springer LNM 1201 (1987), 165-179

Ma T. Mabuchi: Einstein-Kaehler forms, Futaki invariants and convex geometry on toric Fano varieties, Osaka J. Math. 24 (1987), 705-737

PS F. Podestà and A. Spiro: Kaehler manifolds with large isometry group, Osaka J. Math. 36 (1999), 805-833

TZ G. Tian and X. Zhu: A new holomorphic invariant and uniqueness of Kaehler-Ricci solitons, Comment. Math. Helv. 77 (2002), 297-325

timetable:
Thu 30 Sep, 11:15 - 12:15, Sala Conferenze Centro De Giorgi
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