Eiji Inoue

E-mail: eijinoe [at] ms.u-tokyo.ac.jp

I got my doctor degree at University of Tokyo in the end of September 2020.
I am currently a postdoc at University of Tokyo until the end of March 2021.
I will be a postdoc at RIKEN iTHEMS from April 2021. This homepage will expire at that time.

CV and Papers & Talks

Research interest

: Geometry and Analysis

Current main interest

: Canonical metrics in Kähler geometry and K-moduli space.

Keywords: μ-cscK metric (including Kähler-Ricci soliton and extremal metric), μK-stability, optimal destabilizer (non-archimedean canonical metric) in 'μ-framework', moduli theory on Fano varieties

Constant μ-scalar curvature Kähler metric (μ-cscK metric) is a framework unifying cscK metric and Kähler-Ricci soliton, which I proposed in arXiv:1902.00664. The concept of μ-cscK metric possesses a natural parameter λ of freedom, which plays a role reminiscent of `temperature'. Kähler-Ricci soliton appears when λ=2π (with polarization L=-K_X on a Fano manifold X) and extremal metric appears in the limit λ=-∞. The related μK-stability looks simple when λ=0 for general polarization. We may also regard the parameter as a continuity path connecting Kähler-Ricci soliton and extremal metric on Fano manifolds and connecting μ^0-cscK metric and extremal metric for general polarizations. There is also interesting phenomenon analogous to phase transition when λ tends to +∞. I think μ-cscK metric is an attractive part in the extensive framework on weighted cscK metric introduced by Abdellah Lahdili.

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The latest papers and preprints

The moduli space of Fano manifolds with Kähler-Ricci solitons, Advances in Math. Volume 357, 1 Dec. 2019, Article 106841, available also at arXiv:1802.08128.
Constant μ-scalar curvature Kähler metric - formulation and foundational results, preprint arXiv:1902.00664.
Equivariant calculus on μ-character and μK-stability of polarized schemes, preprint arXiv:2004.06393.
Entropies in μ-framework of canonical metrics and K-stability, I -- Archimedean aspect: Perelmna's W-entropy and μ-cscK metrics, preprint arXiv:2101.11197.
Entropies in μ-framework of canonical metrics and K-stability, II -- Non-archimedean aspect: non-archimedean μ-entropy and μK-semistability, in preparation.