Inverses of monomial Cremona maps

2011/05/05 by Peter M. Johnson, Johnson, Peter M.
Mathematics · #11C20 (Secondary) #14E07 (Primary) #15A29 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:11C20 #msc:14E07 #msc:15A29

paper · pdf · doi:10.48550/arxiv.1105.1188

8 pages, 3 tables; v2: corrected some typos, polished parts, added slightly more data, removed part at end for use elsewhere. v3: References updated, minor polishing in several places

openalex publication_date 2011/05/05 · arxiv created 2011/06/07 · arxiv updated 2011/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that monomial Cremona maps of degree d on Pⁿ can have inverses whose degree d' is quite large (for d > 2, d' = ((d-1)ⁿ - 1)/(d-2) occurs), and that the full list of degrees d' does not always form an interval. An easy method for inverting the maps is presented.

Related

• Cremona maps defined by monomials
• Monomial Cremona transformations and toric polar maps
• Classification of the monomial Cremona transformations of the plane
• Counting square free monomial cremona maps
• New Constructions of Cremona Maps