Work

Elliptic curves and birational representation of Weyl groups

Year: 2005

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.math/0511726

Authors: Mitsuaki, Eguchi, Takenawa, Tomoyuki

Institutions: Tokyo University of Marine Science and Technology, The University of Tokyo

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W1522190889

Cites: 5

Cited by: 3

Related to: 10