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Special cubic Cremona transformations of ℙ6 and ℙ7

Giovanni Staglianò
From the journal Advances in Geometry


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.

MSC 2010: 14E05; 14E07; 14J30

  1. Communicated by: I. Coskun


I wish to thank Francesco Russo for valuable communications and for posing to me the problem studied in this paper.


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Received: 2016-08-10
Revised: 2017-03-18
Revised: 2017-04-13
Published Online: 2018-03-20
Published in Print: 2019-04-24

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