De Jonquières transformations in arbitrary dimension. An ideal theoretic view

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.

Keywords:

• Cremona map
• de Jonquières blowup
• downgraded form
• free resolution
• Cohen–Macaulay

2020 Mathematics Subject Classification:

• Primary: 13A30
• 13C14
• 13C15
• 13D02
• 14E07
• Secondary: 13A02