Prym Subvarieties of Jacobians via Schur correspondances between curves
Abstract
Description
Let $π: Z \to X$ be Galois cover of smooth projective curves with Galois group $W$ a Weyl group of a simple Lie group $G$. For a dominant weight $λ$, we consider the intermediate curve $Y_λ= Z/\Stab(λ)$. One can realise a Prym variety $P_λ\subset \Jac(Y_λ)$ and we denote $φ_λ$ the restriction of the principal polarisation of $\Jac(Y_λ)$ upon $P_λ$. For two dominant weights $λ$ and $μ$, we construct a correspondence $Δ_{λμ}$ on $Y_λ\times Y_μ$ and calculate the pull-back of $φ_μ$ by $Δ_{λμ}$ in terms of $φ_λ$.
26 pages
26 pages