3 papers
math.AG2025
Topology of the punctual Hilbert schemes of plane curve singularities with a single Puiseux pair
Masahiro Watari
Piontkowski proved the existence of affine cell decompositions of Jacobian factors of plane curve singularities with a single Puiseux pair. He also provided a combinatorial descrip…
math.NT2024
On a conjecture of Moreno-Frías and Rosales for numerical semigroups
Masahiro Watari
The present paper addresses a semimodule counting conjecture of Moreno-Frías and Rosales for numerical semigroups. Applying Pfister and Steenbrink's Theory for punctual Hilbert sch…
math.AG2024
Motivic Hilbert zeta functions for curve singularities and related invariants
Masahiro Watari
In the present paper, we show that the motivic Hilbert zeta function for a curve singularity yields the generating functions for Euler numbers of punctual Hilbert schemes when any…