论文标题
在偏光份量表面的模量空间上
On moduli spaces of polarized Enriques surfaces
论文作者
论文摘要
我们证明，对于任何$ g \ geq 2 $，étaledouble Cover $ρ_g：\ Mathcal {e} _ {g} \ to \ wideHat {\ Mathcal {\ Mathcal {e}} _ {g} $从moduli space $ \ nathcal $ \ nathcal $ suriques unieliques nirieliques nirieliques nirieliques Moduli空间$ \ wideHat {\ Mathcal {e}} _ {g} $数值两极化的属$ g $ enliques表面与$ \ wideHat {\ mathcal {\ natercal {e}} $ paramiS $ 2 $ 2的不可回值组件相对于不可值得不可减少的组件而被脱节。赫莱克。我们表征了$ \ mathcal {e} _ {g} $的所有不可减至的组件，该$在Enriques表面上的新不变性捆绑包中概括了Cossec引入的$ ϕ $ -Invariant。特别是，我们在$ \ mathcal {e} _g $的不可约组件和满足特定条件的整数的$ 11 $ TUPLAPLE之间获得一对一的对应关系。这原则上可以列出每个$ g \ geq 2 $的$ \ Mathcal {e} _g $的所有不可约组件。
We prove that, for any $g \geq 2$, the étale double cover $ρ_g:\mathcal{E}_{g} \to \widehat{\mathcal{E}}_{g}$ from the moduli space $\mathcal{E}_{g}$ of complex polarized genus $g$ Enriques surfaces to the moduli space $\widehat{\mathcal{E}}_{g}$ of numerically polarized genus $g$ Enriques surfaces is disconnected precisely over irreducible components of $\widehat{\mathcal{E}}_{g}$ parametrizing $2$-divisible classes, answering a question of Gritsenko and Hulek. We characterize all irreducible components of $\mathcal{E}_{g}$ in terms of a new invariant of line bundles on Enriques surfaces that generalizes the $ϕ$-invariant introduced by Cossec. In particular, we get a one-to-one correspondence between the irreducible components of $\mathcal{E}_g$ and $11$-tuples of integers satisfying particular conditions. This makes it possible, in principle, to list all irreducible components of $\mathcal{E}_g$ for each $g \geq 2$.
