The bad locus in the moduli of super Riemann surfaces with Ramond punctures
The bad locus in the moduli of super Riemann surfaces with Ramond punctures
复制标题
具有雷蒙德穿孔的超级黎曼曲面模量的坏轨迹
DOI：
10.1016/j.geomphys.2023.104765
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发表时间：
2023
影响因子：
1.5
通讯作者：
Ott, Nadia
中科院分区：
文献类型：
--
作者：
Donagi, Ron;Ott, Nadia
具有Ramond穿刺的超黎曼曲面的模中的坏轨迹参数化了那些具有多于期望数量的独立闭全纯1-形式的超黎曼曲面。有一个超周期图，它依赖于某些离散的选择。对于每一个这样的选择，周期图都沿着沿着一个包含坏轨迹的除数放大。我们的主要结果是，远离坏轨迹，这些周期图中至少有一个是有限的。换句话说，我们将坏轨迹确定为爆破因子的交集。这个证明将这种情况抽象成线性代数中的一个问题，然后我们解决这个问题。我们还给出了坏轨迹的维数的一些界。
The bad locus in the moduli of super Riemann surfaces with Ramond punctures parametrizes those super Riemann surfaces that have more than the expected number of independent closed holomorphic 1-forms. There is a super period map that depends on certain discrete choices. For each such choice, the period map blows up along a divisor that contains the bad locus. Our main result is that away from the bad locus, at least one of these period maps remains finite. In other words, we identify the bad locus as the intersection of the blowup divisors. The proof abstracts the situation into a question in linear algebra, which we then solve. We also give some bounds on the dimension of the bad locus.