Multiplicity of jet schemes of monomial schemes

TL;DR

This paper investigates the structure of jet schemes of monomial schemes, providing a formula for their multiplicity along each component, especially focusing on reduced monomial hypersurfaces like simple normal crossing divisors.

Contribution

It introduces a formula for the multiplicity of jet schemes of reduced monomial hypersurfaces, advancing understanding of their geometric structure.

Findings

Jet schemes of monomial schemes are equidimensional but not reduced.

A formula for multiplicity along each component of jet schemes is provided.

Results are specifically applied to simple normal crossing divisors.

Abstract

This article studies jet schemes of monomial schemes. They are known to be equidimensional but usually are not reduced. We thus investigate their structure further, giving a formula for the multiplicity along every component of the jet schemes of a general reduced monomial hypersurface (that is, the case of a simple normal crossing divisor).