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Special cubic Cremona transformations of ℙ6 and ℙ7

Authors
  • Staglianò, Giovanni
Type
Published Article
Journal
Advances in Geometry
Publisher
De Gruyter
Publication Date
Mar 20, 2018
Volume
19
Issue
2
Pages
191–204
Identifiers
DOI: 10.1515/advgeom-2018-0001
Source
De Gruyter
Keywords
License
Yellow

Abstract

A famous result of Crauder and Katz (1989) concerns the classification of special Cremona transformations whose base locus has dimension at most two. They also proved that a special Cremona transformation with base locus of dimension three has to be one of the following: 1) a quinto-quintic transformation of ℙ5; 2) a cubo-quintic transformation of ℙ6; or 3) a quadro-quintic transformation of ℙ8. Special Cremona transformations as in Case 1) have been classified by Ein and Shepherd-Barron (1989), while in our previous work (2013), we classified special quadro-quintic Cremona transformations of ℙ8. Here we consider the problem of classifying special cubo-quintic Cremona transformations of ℙ6, concluding the classification of special Cremona transformations whose base locus has dimension three.

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