2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105142Some Weyl group acts on a family of rational varieties obtained by successive blow-ups at $m$ ($m\geq n+2$) points in the projective space $\mpp^n(\mc)$. In this paper we study the case where all the points of blow-ups lie on a certain elliptic curve in $\mpp^n$. Investigating the action of Weyl group on the Picard groups on the elliptic curve and on rational varieties, we show that the action on the parameters can be written as a group of linear transformations on the $(m+1)$-st power of a torus.14 pagesAlgebraic GeometryRepresentation TheoryPrimary 14E07; Secondary 14H52, 14H70text