TY  - JOUR
ID  - Adachi2022
LB  - Adachi2022
AU  - Adachi, Shunya
TI  - Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities
ST  - Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 3
SP  - 361
EP  - 391
DO  - https://doi.org/10.7494/OpMath.2022.42.3.361
UR  - https://doi.org/10.7494/OpMath.2022.42.3.361
AB  - We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degenerate invariant Hermitian forms in terms of that cubic surface. The explicit forms of invariant Hermitian forms are also given. Our result may bring a new insight into the study of the Painlevé differential equations.
KW  - Fuchsian differential equations
KW  - monodromy representation
KW  - monodromy invariant Hermitian form
SN  - 1232-9274
ER  -