A Class of Locally Complete Intersection Multiple Structures on Smooth Algebraic Varieties as Support

TL;DR

This paper introduces a new class of multiple locally complete intersection structures on smooth algebraic varieties, expanding the understanding of their local defining equations and geometric properties.

Contribution

It constructs a broad class of such structures explicitly, generalizing previous specific cases and providing a framework for their analysis.

Findings

Defines a new class of locally complete intersection multiple structures

Provides explicit local equations characterizing these structures

Enhances understanding of their geometric and algebraic properties

Abstract

We give the construction of a class of multiple locally complete intersection structures on a smooth algebraic variety as support. This class contains the structures defined locally by equations of the form $x^n=0$, $y^2=0$, $z=0, >..., u=0$.