Multiplier ideal sheaves and integral invariants on toric Fano manifolds

Abstract

Abstract. We extend Nadel's results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author. Applying our extension we can determine the multiplier ideal subvarieties on toric del Pezzo surfaces which do not admit Kähler-Einstein metrics. We also show that one can define multiplier ideal sheaves for Kähler-Ricci solitons and extend the result of Nadel using the holomorphic invariant defined by Tian and Zhu.

Multiplier ideal sheaves and geometric problems

“…Hence V ⊂ Z + (v), which is a contradiction. As far as the authors know, other applications of Theorem 3.1 except this example had been unknown until [21].…”

Existence of Kähler–Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces

“…In the first two versions of [10] it was claimed that it is the proper transform of the line through P 1 , P 2 that arises. However, this claim has been retracted in the third version.…”

“…However, this claim has been retracted in the third version. We refer the reader to [10] for more details.…”

Multiplier ideal sheaves and the Kähler–Ricci flow on toric Fano manifolds with large symmetry

“…In [11], Futaki and the author investigated the relationship between the multiplier ideal subvariety derived from the continuity method on toric Fano manifolds and Futaki invariant, and calculated the multiplier ideal subvariety on a simple example. On the other hand, the relationship between the multiplier ideal sheaves and the Kähler-Ricci flow has recently been studied.…”

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The purpose of this paper is to calculate the support of the multiplier ideal sheaves derived from the Kähler-Ricci flow on certain toric Fano manifolds with large symmetry. The early idea of this paper has already been in Appendix of [11].

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