Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing weighted stable elliptic surfaces — elliptic fibrations with section and marked fibers each weighted between zero and one. Moreover, we show that the domain of weights admits a wall and chamber structure, describe the induced wall‐crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical result is a proof of invariance of log plurigenera for slc elliptic surface pairs with arbitrary weights.

中文翻译：

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加权稳定椭圆曲面的模数和对数多变数的不变性

受Hassett加权尖的稳定曲线的激励，我们使用对数最小模型程序构造参数化加权稳定椭圆曲面的紧凑模空间-椭圆纤维的截面纤维和标记纤维的权重在零和一之间。此外，我们证明了权重域允许具有壁和腔结构，描述了随着权重矢量变化而在模空间上引起的墙交叉形态，并描述了出现在模空间边界上的表面。主要技术结果是对任意权重的slc椭圆形表面对的对数多变数的不变性的证明。