Jet schemes of toric surfaces (a short version)

TL;DR

This paper investigates the structure of jet schemes of toric surfaces, revealing a connection between their irreducible components and the surface's minimal resolution for large jet orders.

Contribution

It explicitly determines the irreducible components of jet schemes of toric surfaces and links their count to the exceptional divisors in the minimal resolution.

Findings

Identified irreducible components of jet schemes for toric surfaces.

Established a relationship between jet scheme components and minimal resolution.

Provided explicit descriptions for large jet orders.

Abstract

For $m\in \IN, m\geq 1,$ we determine the irreducible components of the $m-th$ jet scheme of a toric surface $S.$ For $m$ big enough, we connect the number of a class of these irreducible components to the number of exceptional divisors on the minimal resolution of $S.$