RELATIVE TWISTED KÄHLER-RICCI FLOWS ON FAMILIES OF COMPACT KÄHLER MANIFOLDS
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초록
Let p : X → D be a proper surjective holomorphic submersion where X is a Kähler manifold and D is the unit disc in ℂ. Let Ω be a d-closed semi-positive real (1, 1)-form on X. If each Xs := p-1(s) for s ∈ D satisfies − c 1 ( X s ) + Ω ∣ X s is Kähler, then the Kähler-Ricci flow twisted by Ω ∣ X s has a long time solution by Cao's theorem. This family of twisted Kähler-Ricci flows induces a relative Kähler form ω(t) on the total space X. In this paper, we prove that the positivity of ω(t) is preserved along the twisted Kähler-Ricci flow.
Abstract
Let p : X → D be a proper surjective holomorphic submersion where X is a Kähler manifold and D is the unit disc in ℂ. Let Ω be a d-closed semi-positive real (1, 1)-form on X. If each Xs := p-1(s) for s ∈ D satisfies − c 1 ( X s ) + Ω ∣ X s is Kähler, then the Kähler-Ricci flow twisted by Ω ∣ X s has a long time solution by Cao's theorem. This family of twisted Kähler-Ricci flows induces a relative Kähler form ω(t) on the total space X. In this paper, we prove that the positivity of ω(t) is preserved along the twisted Kähler-Ricci flow.
참고문헌 (7)
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