Birational map

For example, we still don’t know if it has the structure of an algebraic group of infinite dimension. In this paper, we will construct the Cremona group functor, calculate its Lie algebra and show that its Lie algebra is simple.

11p tamynhan9 02-12-2020 6 1   Download

In the article, we see that the birational maps of degree d of the projective space Pn k form a locally closed subvariety of the projective space P(Sdn11), denoted Crd(n). In this paper, we will construct the notion of extended degree of rational maps, then we obtain the functor crd(n) that represents the variety Crd(n).

8p tamynhan9 02-12-2020 16 2   Download

A natural and simple question asked is: Does the Cremona group Cr(n) admit a structure that is of an algebraic group of infinite dimension. This is still an open question because we don’t know if the set Cr≤d(n) of birational maps of degree ≤ d admits a structure of the algebraic variety.

9p tamynhan8 04-11-2020 10 1   Download