On special quadratic birational transformations whose base locus has dimension at most three

TL;DR

This paper investigates special quadratic birational transformations from projective space to a variety, focusing on cases where the base locus is smooth, irreducible, and of dimension at most three, with an emphasis on the regularity of the image.

Contribution

It characterizes and analyzes quadratic birational transformations with low-dimensional smooth base loci and regular images, expanding understanding of their structure and properties.

Findings

Classification of transformations with base locus dimension ≤ 3

Conditions for the regularity of the image variety

Insights into the structure of the base locus and image

Abstract

We study birational transformations P^n--->S \subseteq P^N defined by linear systems of quadrics whose base locus is smooth and irreducible of dimension \leq3 and whose image S is sufficiently regular.