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.
and Papers & Talks
: Geometry and Analysis
Current main interest
: Canonical metrics in Kähler geometry and K-moduli space.
: 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.
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.
I'll be there
Prof. Akito Futaki
Prof. Shigeharu Takayama