Examples of special quadratic birational transformations into complete intersections of quadrics

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• 作者：Giovanni Staglianò ; ^{giovannistagliano@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：14E05 ; 14Q15 ; 14J30
• 刊名：Journal of Symbolic Computation
• 出版年：2016
• 出版时间：May-June 2016
• 年：2016
• 卷：74
• 期：Complete
• 页码：635-649
• 全文大小：439 K

文摘

In our previous works ( and ), we provided a finite list of properties characterizing all potential types of quadratic birational transformations of a projective space into a factorial variety, whose base locus is smooth and irreducible. However, some existence problems remained open. Among them one had to prove that the image of a given transformation was factorial, but in two particular situations, even the mere existence of the transformation was left as an open problem. In this paper, we use computer algebra methods to construct explicitly four examples of such transformations; two of them were among those for which it was not known that the image was factorial, and the other two show the existence of the two above referred transformations.