De Jonquières transformations in arbitrary dimension. An ideal theoretic view. Issue 9 (2nd September 2022)

• Record Type: Journal Article
• Authors: Ramos, Zaqueu; Simis, Aron
• Is Part Of: Communications in algebra. Volume 50:Issue 9(2022)
• Page Start: 4095
• Page End: 4108
• Publication Date: 2022-09-02
• Subjects: Cremona map -- de Jonquières blowup -- downgraded form -- free resolution -- Cohen–Macaulay; Primary: 13A30 -- 13C14 -- 13C15 -- 13D02 -- 14E07 -- Secondary: 13A02; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2057519
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: A generalization of the plane de Jonquières transformation to arbitrary dimension is studied, with an eye for the ideal theoretic side. In particular, one considers structural properties of the corresponding base ideal and of its defining relations. Useful throughout is the idea of downgraded sequences of forms, a tool considered in many sources for the rounding-up of ideals of defining relations. The emphasis here is on the case where the supporting Cremona transformation of the de Jonquières transformation is the identity map. In this case we give some results on the homological behavior of the graph of the transformation.