Examples of special quadratic birational transformations into complete intersections of quadrics. (May 2016)

• Record Type: Journal Article
• Authors: Staglianò, Giovanni
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 635
• Page End: 649
• Publication Date: 2016-05
• Subjects: 14E05 -- 14Q15 -- 14J30; Birational transformation -- Base locus -- Threefold; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.11.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In our previous works (Staglianò 2012, 2013 ), 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.