2021/09/22 by Zaqueu Ramos, Aron Simis, Ramos, Zaqueu +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2109.10479
openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 establish aspects of the homological behavior of the graph of the transformation.