Transformações de Cremona de P4 que se fatoram através de projeções de uma interseção completa de três quádricas de P7

Abstract

In this work, we consider the complete intersection (...) of the quadric hipersurfaces of(...), containing two 2-planes (...) and (...), with X is smooth. We fix two 4-planes (...) with(...). We prove that a transformation(...) which factorizes through projections of X with center in (...) and (...) is a Cremona transformation of degree 4, whose inverse alsohas degree 4. Moreover, if (...), then T is a determinantal Cremona transformation, if (...) (is a line), then T is a De Jonquières Cremona transformation and if (...) (is a point), then T is neither determinantal nor De Jonquières.