Moduli of weighted stable elliptic surfaces and invariance of log plurigenera
Moduli of weighted stable elliptic surfaces and invariance of log plurigenera
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DOI：
10.1112/plms.12387
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发表时间：
2017-02
影响因子：
1.8
通讯作者：
Kenneth Ascher;Dori Bejleri
中科院分区：
文献类型：
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作者：
Kenneth Ascher;Dori Bejleri
在Hassett加权点稳定曲线的激励下，我们使用对数最小模型程序构造了参数化加权稳定椭圆曲面的紧模空间——截面纤维和标记纤维的加权在0到1之间的椭圆纤维。此外，我们证明了权域允许一个壁室结构，描述了随着权向量的变化模空间上诱导的壁交叉态射，并描述了出现在模空间边界上的曲面。主要的技术成果是证明了任意权值slc椭圆曲面对的多生对数不变性。
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.