Equivalent birational embedding IV: reduced varieties

TL;DR

This paper revises known results on Cremona equivalence for reduced projective schemes, extending previous work to broader cases and establishing a general contractibility result for unions of rational subvarieties.

Contribution

It extends the main result of [MP09] to reduced schemes and proves a general contractibility theorem for unions of rational subvarieties.

Findings

Extended Cremona equivalence results to reduced schemes

Proved a general contractibility result for unions of rational subvarieties

Revised known results on Cremona equivalence

Abstract

Two reduced projective schemes are said to be Cremona equivalent if there is a Cremona map that maps one in the other. In this paper I revise some of the known results about Cremona equivalence and extend the main result of [MP09] to reduced schemes. This allows to prove a very general contractibility result for union of rational subvarieties.