arXiv 2103.168932021-03math.AG

病毒感染、电晕表面和稳定表面的模空间中的额外分量

Virus infections, Corona surfaces, and extra components in the moduli space of stable surfaces

Sönke Rollenske

备注：: Disclaimer: While the language and the pictures in this note are inspired by current events, the actual content is a result of pure mathematics not related to medical research. 9 pages, 11 figures. v2: updated result to distinguish connected components

摘要：

我们构建的例子，非smoothable稳定的表面，我们称之为电晕表面，不变量在很宽的范围内，包括所有可能的不变量的光滑极小曲面的一般类型，但非标准的第二plurigenus。我们证明了稳定曲面$\overline{\mathfrak M}_{k,l}$的模空间具有最少的第二类连通分支，特别是在相同的不变量下，它总是比Gieseker模空间具有更多的不可约分支.

英文摘要：

We construct examples of non-smoothable stable surfaces, that we call Corona surfaces, with invariants in a wide range comprising all possible invariants of smooth minimal surfaces of general type but non-standard second plurigenus. We deduce that the moduli space of stable surfaces $\overline{\mathfrak M}_{k,l}$ has least $k-l+2$ connected components distinguished by the second plurigenus and, in particular, it always has more irreducible components than the Gieseker moduli space with the same invariants.

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