Fano schemes of complete intersections in toric varieties
Fano schemes of complete intersections in toric varieties
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DOI：
10.1007/s00209-021-02809-4
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发表时间：
2019-10
影响因子：
0.8
通讯作者：
N. Ilten;Tyler L. Kelly
中科院分区：
文献类型：
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作者：
N. Ilten;Tyler L. Kelly
研究了射影环面簇中完全交的Fano格式。我们的策略是在Ilten和Zotine研究的不可约分解的基础上分解成封闭的子方案。我们为这些子方案定义了“期望维数”，它总是给出实际维数的下限。在额外的假设下，我们证明了这些子方案是非空的，光滑的期望尺寸。利用交理论的工具，我们可以应用这些结果来计算期望维数为零时X中线性子空间的个数。
We study Fano schemesfor complete intersectionsXin a projective toric variety. Our strategy is to decomposeinto closed subschemes based on the irreducible decomposition ofas studied by Ilten and Zotine. We define the “expected dimension” for these subschemes, which always gives a lower bound on the actual dimension. Under additional assumptions, we show that these subschemes are non-empty and smooth of the expected dimension. Using tools from intersection theory, we can apply these results to count the number of linear subspaces inXwhen the expected dimension ofis zero.