3 citations · 5 across the 4 of their papers we have counts for
5 papers · 1 filter
The Local Nash problem on arc families of singularities
Shihoko Ishii
This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to…
Arcs, valuations and the Nash map
Shihoko Ishii
This paper gives a map from the set of families of arcs on a variety to the set of valuations on the rational function field of the variety We characterize a family of arcs which c…
The arc space of a toric variety
Shihoko Ishii
The Nash problem on arc families is affirmatively answered for a toric variety by Ishii and Kollar's paper which also shows the negative answer for general case. The Nash problem i…
The Nash problem on arc families of singularities
Shihoko Ishii, János Kollár
Nash proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that occurs on every resolution. He asked if the conve…
The geometric minimal models of analytic spaces
S. Ishii, P. Milman
This paper shows that an analytic space has a unique maximal model through which every proper surjective morphism from a non-singular analytic space to factors. This is cal…