Counting square-free monomial Cremona maps (Q6116632)

The paper under review is focused on the investigation of special Cremona transformations of \( \mathbb{P}^{n-1} \) called square-free Cremona maps. The important new result proved in the paper discusses the equivalence classes of square-free monomial Cremona transformations of \( \mathbb{P}^5\). The particular case of such cubic Cremona transformations is considered in detail. The same classification task is solved for quadratic square-free Cremona maps of \( \mathbb{P}^{n-1}\) when the number \(n=7,8,9.10,11\), and for cubic square-free Cremona maps of \( \mathbb{P}^6 \).