论文标题
在嵌入式Enriques歧管上平滑多个结构
Smoothing of multiple structures on embedded Enriques manifolds
论文作者
论文摘要
我们表明，鉴于在足够大的投影空间中嵌入了索引$ d $的Enriques歧管，将存在嵌入的多个结构，这些结构具有串联束同构与通用覆盖地图的跟踪零模块，通用覆盖物是Hyperkähller或Calabi-yau歧管。然后，我们表明这些多个结构（也称为$ d $ - ropes）可以平滑以平滑Hyperkähler或Calabi-yau歧管。因此，我们获得了嵌入在同一投影空间中的Hyperkähler（或Calabi-yau）的平坦家族，该歧管在索引$ d $的给定Enriques歧管上退化为嵌入式$ d $ rope结构。以上表明，嵌入式Enriques歧管上的这些$ d $ - rope结构是希尔伯特方案的点，其中包含上述家族的纤维。我们表明，当$ d = 2 $时，它们是希尔伯特计划的平滑点。
We show that given an embedding of an Enriques manifold of index $d$ in a large enough projective space, there will exist embedded multiple structures with conormal bundle isomorphic to the trace zero module of the universal covering map, the universal cover being either a hyperkähler or a Calabi-Yau manifold. We then show that these multiple structures (also known as $d$-ropes) can be smoothed to smooth hyperkähler or Calabi-Yau manifolds respectively. Hence we obtain a flat family of hyperkähler (or Calabi-Yau) manifolds embedded in the same projective space which degenerates to an embedded $d$-rope structure on the given Enriques manifold of index $d$. The above shows that these $d$-rope structures on the embedded Enriques manifold are points of the Hilbert scheme containing the fibres of the above family. We show that they are smooth points of the Hilbert scheme when $d=2$.
