Hiraku Kawanoue
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View article: On the extended Catalan arrangement of type $B_\ell$
On the extended Catalan arrangement of type $B_\ell$ Open
We give an explicit formula for the generators of the logarithmic vector field of the coning of the extended Catalan arrangement of type $B_\ell$.
View article: Cokernels of the Euler restriction map of logarithmic derivation modules
Cokernels of the Euler restriction map of logarithmic derivation modules Open
There are two restriction maps of the logarithmic modules of plane arrangements in a three dimensional vector space. One is the Euler restriction and the other is the Ziegler restriction. The dimension of the cokernel of the Ziegler restri…
View article: On Abel's Problem about Logarithmic Integrals in Positive Characteristic
On Abel's Problem about Logarithmic Integrals in Positive Characteristic Open
Linear differential equations with polynomial coefficients over a field $K$ of positive characteristic $p$ with local exponents in the prime field have a basis of solutions in the differential extension $\mathcal{R}_p=K(z_1, z_2, \ldots)(\…
View article: On a conjecture of Feigin, Wang and Yoshinaga
On a conjecture of Feigin, Wang and Yoshinaga Open
We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).
View article: A new strategy for resolution of singularities in the monomial case in positive characteristic
A new strategy for resolution of singularities in the monomial case in positive characteristic Open
According to our approach for resolution of singularities in positive characteristic (called the Idealistic Filtration Program, alias the I.F.P. for short) the algorithm is devided into the following two steps: Step 1. Reduction of the gen…