Elliptic curves and birational representation of Weyl groups

Details Elliptic curves and birational representation of Weyl groups Elliptic curves and birational representation of Weyl groups

2005-11-30

arxiv.org/abs/math/0511726v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

Some 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.

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