Toshizumi Fukui

activity

20072025

most citedHeight functions on Whitney umbrellas

9 citations · 14 across the 11 of their papers we have counts for

collaborators

12 papers

math.DG2025

Curvature criteria of A-simple singularities R,0-> R^2,0 and their parallel curves

Toshizumi Fukui, Saiki Hoshino

We introduce the notion of curvature parameters for singular plane curves with finite multiplicities and define the notion of curvatures for them. We then provide criteria to deter…

math.DG2024

Height functions on singular surfaces parameterized by smooth maps $A$ -equivalent to $S_{k}$ , $B_{k}$ , $C_{k}$ and $F_{4}$

Toshizumi Fukui, Masaru Hasegawa

We describe singularities of height functions on singular surfaces in $R^{3}$ parameterized by smooth map-germs $A$ -equivalent to one of $S_{k}$ , $B_{k}$ , $C_{k}$ and $F…

math.DG2024

Distance squared functions on singular surfaces parameterized by smooth maps $A$ -equivalent to $S_{k}$ , $B_{k}$ , $C_{k}$ and $F_{4}$

Toshizumi Fukui, Masaru Hasegawa

We describe singularities of distance squared functions on singular surfaces in $R^{3}$ parameterized by smooth map-germs $A$ -equivalent to one of $S_{k}$ , $B_{k}$ , $C…

math.DG2023

Versality of Rotation Unfolding of Folding Maps for Surfaces in $R^{3}$

Toshizumi Fukui, Atsuki Hiramatsu

We introduce the rotation unfolding of the folding map of a surface in $R^{3}$ , and investigate its $A$ -vesality. The rotation unfolding is a 2-parameter unfolding…

math.AG2018★ 1 cited

Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets

Jean-Baptiste Campesato, Toshizumi Fukui, Krzysztof Kurdyka +1

We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real al…

math.AG2014

Mixed Łojasiewicz exponents, log canonical thresholds of ideals and bi-Lipschitz equivalence

Carles Bivià-Ausina, Toshizumi Fukui

We study the Łojasiewicz exponent and the log canonical threshold of ideals of $O_{n}$ when restricted to generic subspaces of $C^{n}$ of different dimensions. We obta…

Curvature criteria of A-simple singularities R,0-> R^2,0 and their parallel curves

Height functions on singular surfaces parameterized by smooth maps A-equivalent to Sk​, Bk​, Ck​ and F4​

Distance squared functions on singular surfaces parameterized by smooth maps A-equivalent to Sk​, Bk​, Ck​ and F4​

Versality of Rotation Unfolding of Folding Maps for Surfaces in R3

Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets

Mixed Łojasiewicz exponents, log canonical thresholds of ideals and bi-Lipschitz equivalence

Height functions on singular surfaces parameterized by smooth maps $A$ -equivalent to $S_{k}$ , $B_{k}$ , $C_{k}$ and $F_{4}$

Distance squared functions on singular surfaces parameterized by smooth maps $A$ -equivalent to $S_{k}$ , $B_{k}$ , $C_{k}$ and $F_{4}$

Versality of Rotation Unfolding of Folding Maps for Surfaces in $R^{3}$