8 research outputs found
Stability conditions and positivity of invariants of fibrations
We study three methods that prove the positivity of a natural numerical
invariant associated to parameter families of polarized varieties. All
these methods involve different stability conditions. In dimension 2 we prove
that there is a natural connection between them, related to a yet another
stability condition, the linear stability. Finally we make some speculations
and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus
Hulek on the occasion of his 60-th birthda
Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure
We further develop the numerical algorithm for computing the gauge connection
of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In
particular, recent work on the generalized Donaldson algorithm is extended to
bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the
computation depends only on a one-dimensional ray in the Kahler moduli space,
it can probe slope-stability regardless of the size of h^{1,1}. Suitably
normalized error measures are introduced to quantitatively compare results for
different directions in Kahler moduli space. A significantly improved numerical
integration procedure based on adaptive refinements is described and
implemented. Finally, an efficient numerical check is proposed for determining
whether or not a vector bundle is slope-stable without computing its full
connection.Comment: 38 pages, 10 figure
An investigation in the correlation between Ayurvedic body-constitution and food-taste preference
Extremal metrics on ruled manifolds
In this paper, we consider a compact KÀhler manifold with extremal KÀhler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal KÀhler metric is liftable to the bundle and if the bundle is relatively stable with respect to the action of automorphisms of the manifold, then there exist extremal KÀhler metrics on the projectivization of the dual vector bundle. © 2014 Elsevier Inc
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Extremal metrics on ruled manifolds
In this paper, we consider a compact KÀhler manifold with extremal KÀhler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal KÀhler metric is liftable to the bundle and if the bundle is relatively stable with respect to the action of automorphisms of the manifold, then there exist extremal KÀhler metrics on the projectivization of the dual vector bundle. © 2014 Elsevier Inc