# Counting Square free Cremona monomial maps

@article{Costa2015CountingSF, title={Counting Square free Cremona monomial maps}, author={Barbara Costa and Thiago Dias and Rodrigo Gondim}, journal={arXiv: Commutative Algebra}, year={2015} }

We use combinatorics tools to reobtain the classification of monomial quadratic Cremona transformations in any number of variables given in \cite{SV2} and to classify and count square free cubic Cremona maps with at most six variables, up to isomorphism.

## References

SHOWING 1-9 OF 9 REFERENCES

On the monomial birational maps of the projective space

- Mathematics
- 2003

We describe the group structure of monomial Cremona transformations. It follows that every element of this group is a product of quadratic monomial transformations, and geometric descriptions in…

Combinatorics of Cremona monomial maps

- Mathematics, Computer ScienceMath. Comput.
- 2012

A simple integer matrix theoretic proof that the inverse of a Cremona monomial map is also defined by monomials of fixed degree, and moreover, the set ofmonomials defining the inverse can be obtained explicitly in terms of the initial data.

Cremona maps defined by monomials

- Mathematics
- 2011

Cremona maps defined by monomials of degree 2 are thoroughly analyzed and classified via integer arithmetic and graph combinatorics. In particular, the structure of the inverse map to such a monomial…

Geometry of the Plane Cremona Maps

- Mathematics
- 2001

Preliminaries.- Plane Cremona maps.- Clebsch's theorems and jacobian.- Composition.- Characteristic matrices.- Total principal and special homaloidal curves.- Inverse Cremona map.- Noether's…

Linear syzygies and birational combinatorics

- Mathematics
- 2005

Let F be a finite set of monomials of the same degree d ≥ 2 in a polynomial ring R = k[x1,…, xn] over an arbitrary field k. We give some necessary and/or sufficient conditions for the birationality…

On birational monomial transformations of plane

- Computer Science, MathematicsInt. J. Math. Math. Sci.
- 2004

For every birational monomial transformations of the form φ, this work proves a formula, which represents the transformation φ as a product of generators of the group.

Constraints for the normality of monomial subrings and birationality

- Mathematics
- 2002

Let k be a field and let F C k[x 1 ,...,x n ] be a finite set of monomials whose exponents lie on a positive hyperplane. We give necessary conditions for the normality of both the Rees algebra R[Ft]…

Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics 238

- 2001