Arata KOMYO 
Arata KOMYO
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Algebra
Associate Professor 
Building B, Room 326

Research Field :
Compactifications of character varieties, isomonodromic deformations


Research Summary :
Motivated by the conjectures on compactifications of character varieties
due to Simpson and on their Mixed Hodge structures due to Hausel et al, I
study compactifications of some examples of character varieties. Recently,
I also study isomonodromic deformations by the moduli theory of stable
parabolic connections.


Primary Publications : 

Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces (with MasaHiko Saito), accepted in Kyoto Journal of Mathematics. (arXiv:math/1611.00971)

Mixed Hodge structures of the moduli spaces of parabolic connections, Nagoya Math. J. 225, 185206 (2017).

An explicit description of the relative $\mathrm{SL}(4,\mathbb{C})$character variety of the projective line, Manuscripta Math., 150, no. 3, 441464 (2016).

On compactifcations of character varieties of $n$punctured projective line, Ann. Inst. Fourier (Grenoble), 65 no. 4, 14931523, (2015).


