30 citations · 77 across the 13 of their papers we have counts for
16 papers
Metric entropy of Kähler potentials
Tomoyuki Hisamoto
We prove sharp metric entropy estimates for spaces of Kähler potentials. In complex dimension , normalized potentials have Kolmogorov entropy of order $\e^{-n}$ in the backgroun…
The Miyaoka-Yau inequality and the delta invariant for Fano varieties I -klt Fano case-
Tomoyuki Hisamoto, Masataka Iwai
We establish the following Miyaoka-Yau inequality for any -dimensional klt Fano variety , possibly K-unstable, in terms of its delta invariant: \[\left(2(n+1)\widehat{c}_2(X)…
Continuity method for the Mabuchi soliton on the extremal Fano manifolds
Tomoyuki Hisamoto, Satoshi Nakamura
We run the continuity method for Mabuchi's generalization of Kähler-Einstein metrics, assuming the existence of an extremal Kähler metric. It gives an analytic proof (without minim…
On the Miyaoka-Yau inequality for manifolds with nef anti-canonical line bundle
Tomoyuki Hisamoto
Based on the recent work of K.~Zhang, we discuss the Miyaoka-Yau type inequality for projective manifolds with nef anti-canonical line bundle, assuming the lower bound of the delta…
Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold
Tomoyuki Hisamoto
For a Fano manifold, We consider the geometric quantization of the Kähler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is establis…
Mabuchi's soliton metric and relative D-stability
Tomoyuki Hisamoto
For Fano manifolds T. Mabuchi introduced a generalization of the Kähler-Einstein metric, which is characterized as the critical point of the Ricci-Calabi functional. We show that a…
Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold
Tomoyuki Hisamoto
S. K. Donaldson asked whether the lower bound of the Calabi functional is achieved by a sequence the normalized Donaldson-Futaki invariants. We answer the question for the Ricci cu…
The inverse Monge-Ampere flow and applications to Kahler-Einstein metrics
Tristan C. Collins, Tomoyuki Hisamoto, Ryosuke Takahashi
We introduce the inverse Monge-Ampere flow as the gradient flow of the Ding energy functional on the space of Kahler metrics in for . We prove the long-time e…
Stability and coercivity for toric polarizations
Tomoyuki Hisamoto
We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are no…
Orthogonal projection of a test configuration to vector fields
Tomoyuki Hisamoto
Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associat…
Uniform K-stability and asymptotics of energy functionals in Kähler geometry
Sébastien Boucksom, Tomoyuki Hisamoto, Mattias Jonsson
Consider a polarized complex manifold (X,L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X,L). For most of the common functionals in…
Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs
Sébastien Boucksom, Tomoyuki Hisamoto, Mattias Jonsson
The purpose of the present paper is to set up a formalism inspired from non-Archimedean geometry to study K-stability. We first provide a detailed analysis of Duistermaat-Heckman m…
On the limit of spectral measures associated to a test configuration
Tomoyuki Hisamoto
We apply the integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt--Nyström so that t…
Remarks on -jet extension and extension of singular Hermitian metric with semipositive curvature
Tomoyuki Hisamoto
We give a new variant of -extension theorem for the jets of holomorphic sections and discuss the relation between the extension problem of singular Hermitian metrics with semi…
Restricted Bergman kernel asymptotics
Tomoyuki Hisamoto
In this paper, we investigate a restricted version of Bergman kernels for high powers of a big line bundle over a smooth projective variety. The geometric meaning of the leading te…
On the volume of graded linear series and Monge-Ampère mass
Tomoyuki Hisamoto
We give an analytic description for the volume of a graded linear series.