基于曲线间Schur对应的Jacobian的Prym子簇
Prym Subvarieties of Jacobians via Schur correspondances between curves
摘要：
设$π: Z \to X$是光滑射影曲线的Galois覆盖，Galois群$W$是单李群$G$的Weyl群.对于主导权重$λ$，我们考虑中间曲线$Y_λ= Z/\Stab(λ)$。人们可以实现一个Prym簇$P_λ\subset \Jac(Y_λ)$，我们将$\Jac(Y_λ)$的主极化限制在$P_λ$上表示为$φ_λ$。对于两个主导权重$λ$和$μ$，我们在$Y_λ\times Y_μ$上构造了一个对应的$Δ_{λμ}$，并根据$φ_λ$计算了$Δ_{λμ}$对$φ_μ$的拉回。
英文摘要：
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 $φ_λ$.
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