# De Jonqui\`eres transformations in arbitrary dimension. An ideal theoretic view

@inproceedings{Ramos2021DeJT, title={De Jonqui\`eres transformations in arbitrary dimension. An ideal theoretic view}, author={Zaqueu Ramos and Aron Simis}, year={2021} }

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… Expand

#### References

SHOWING 1-10 OF 19 REFERENCES

Plane Cremona maps: saturation, regularity and fat ideals

- Mathematics
- 2011

One studies plane Cremona maps from the point of view of the underlying base ideal, focusing on the algebraic and homological properties of the latter. The {\em leitmotiv} driving a substantial… Expand

Cremona transformations and some related algebras

- Mathematics
- 2004

Abstract One proves a general characteristic-free criterion for a rational map between projective varieties to be birational in terms of ideal-theoretic and modulo-theoretic conditions. This… Expand

On the homology of two-dimensional elimination

- Computer Science, Mathematics
- J. Symb. Comput.
- 2008

A computer-assisted method is introduced which succeeds, in degree @?5, in producing the full sets of equations of the ideals, and answers affirmatively some questions raised by Cox. Expand

A characteristic-free criterion of birationality

- Mathematics
- 2012

Abstract One develops ab initio the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A virtual numerical invariant… Expand

Cremona Maps of de Jonquières Type

- Mathematics
- Canadian Journal of Mathematics
- 2015

Abstract This paper is concerned with suitable generalizations of a plane de Jonquières map to higher dimensional space ${{\mathbb{P}}^{n}}$ with $n\,\ge \,3$ . For each given point of… Expand

The ubiquity of Sylvester forms in almost complete intersections

- Mathematics
- 2014

We study the structure of the Rees algebra of almost complete intersection ideals of finite colength in low-dimensional polynomial rings over fields. The main tool is a mix of Sylvester forms and… Expand

Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations

- Computer Science, Mathematics
- Comput. Aided Geom. Des.
- 2010

A minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface and can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution. Expand

On a conjecture of Vasconcelos via Sylvester forms

- Computer Science, Mathematics
- J. Symb. Comput.
- 2016

It is shown that the Rees algebra has a natural quasi-homogeneous structure and its presentation ideal is generated by explicit Sylvester forms, thus providing an affirmative partial answer to a conjecture of W. Vasconcelos. Expand

Les transformations de Cremona stellaires

- Mathematics
- 2000

We construct the Cremona transformations of Pn satisfying the following property: there exist P1, P2 ∈ Pn such that the image of all straight lines through P1 are straight lines through P2. We… Expand

BLOWUPS AND FIBERS OF MORPHISMS

- Mathematics
- Nagoya Mathematical Journal
- 2016

Our object of study is a rational map defined by homogeneous forms $g_{1},\ldots ,g_{n}$ , of the same degree $d$ , in the homogeneous coordinate ring $R=k[x_{1},\ldots ,x_{s}]$ of… Expand