The arc space of a toric variety

By S. Ishii. 2003

72 citations recorded by the source corpus.

Abstract 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 is one of questions about the relation between arc families and valuations. In this paper, the relation is described clearly for a toric variety. The arc space of a toric variety admits an action of the group scheme determined by the torus. Each orbit on the arc space corresponds to a lattice point in the cone and therefore corresponds to a toric valuation. The dominant relation among the orbits is described in terms of the lattice points. As a corollary, we obtain the answer to the embedded version of the Nash problem for an invariant ideal on a toric variety.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eca9c4a8800ab0b075fbd5da355bf206df5e19e4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Tommaso de Fernex
2. S. Ishii
3. L. Ein
4. Chi Li
5. Karl Schwede
6. Mattias Jonsson
7. C. Favre
8. S. Boucksom

In Discrete Mathematics and Combinatorics

1. L. Ein
2. Tommaso de Fernex

In Geometry and Topology

1. Tommaso de Fernex
2. S. Ishii
3. L. Ein
4. M. Mustaţă
5. H. Blum
6. Chi Li
7. Karl Schwede
8. Mattias Jonsson

Citations in the corpus

• Divisorial Valuations via Arcs (2007, background): “where Tm ∼= Cnm × (C∗)n acts on Xm ([ I1 , Proposition 2.6]), and T∞ is the pro-scheme”