Fibres of embedding dimension 2 in generic projections

TL;DR

This paper studies fibers of generic projections of varieties with small local embedding dimension, proving they are reduced and correspond to ordinary multiple points under certain conditions.

Contribution

It establishes that fibers with local embedding dimension at most 2 are reduced and their images are ordinary multiple points, under verifiable assumptions.

Findings

Fibers of local embedding dimension ≤ 2 are reduced.

Images of such fibers are ordinary multiple points.

The results apply to a broad class of generic projections.

Abstract

We consider a general fibre of given length in a generic projection of a va- riety. Under the assumption that the fibre is of local embedding dimension 2 or less, an assumption which can be checked in many cases, we prove that the fibre is reduced and its image on the projected variety is an ordinary multiple point.