Eiji Inoue

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

I am a Ph.D. student of Graduate School of Mathematical Sciences, University of Tokyo.
I am now in Tokyo.

CV and Papers & Talks

Research interest

: Geometry and Analysis

Current main interest

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

Keywords: moduli space of Fano varieties, μ-cscK (including Kähler-Einstein metric, cscK, Kähler-Ricci soliton and extremal metric), μK-stability, optimal destabilizer in 'μ-framework'

Constant μ-scalar curvature Kähler metric (μ-cscK) is a framework unifying cscK and Kähler-Ricci soliton, which I proposed in arXiv:1902.00664. An intriguing aspect of μ-cscK is that the equation of μ-cscK is naturally parametrized by a real number λ and its behavior deforms as λ varies. While the equation is simple when λ=0, Kähler-Ricci soliton appears when λ=2π (with polarization L=-K_X) and extremal metric appears in the limit λ=-∞. The parameter may be regarded as a continuity path connecting Kähler-Ricci soliton and extremal metric (or connecting μ^0-cscK and extremal metric for general polarizations). We can also observe strange phenomenon like phase transition when λ tends to +∞. I think μ-cscK is an attractive part in the extensive framework on weighted cscK introduecd 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.

Schedules

Talks