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Let us consider a projective manifold and a smooth volume form on . We define the gradient flow associated to the problem of -balanced metrics in the quantum formalism, the -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the -balancing flow converges towards a natural flow in Kähler geometry, the -Kähler flow. We also prove the long time existence of the -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing the...
We generalize the work of Jian Song by computing the α-invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the computation of the log canonical threshold of monomial ideals to give the log canonical threshold of any non-negatively curved singular hermitian metric on the line bundle, and deduce the α-invariant from this.
Let be a connected complex Lie group, a closed, complex subgroup of and
. Let be the radical and a maximal semisimple subgroup of . Attempts
to construct examples of noncompact manifolds homogeneous under a nontrivial
semidirect product with a not necessarily -invariant Kähler metric
motivated this paper. The -orbit in is Kähler. Thus is an
algebraic subgroup of [4]. The Kähler assumption on ought to imply the -action
on the base of any homogeneous fibration is algebraic...
We establish new results on weighted -extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.
We prove that Kummer threefolds with algebraic dimension have Kodaira dimension 0.
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