Dimension of the space of conics on a Fano hypersurface
Dimension of the space of conics on a Fano hypersurface
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Fano 超曲面上二次曲线空间的维数
DOI：
10.1016/j.jpaa.2021.106970
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发表时间：
2022
影响因子：
0.8
通讯作者：
Furukawa Katsuhisa
中科院分区：
文献类型：
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作者：
Kentaro Nakamura;Kentaro Nakamura;中村 健太郎;Furukawa Katsuhisa
R. Beheshti证明了对于复数域C上次数为108的光滑Fano超曲面X，位于X中的线的空间的维数等于期望维数。研究了X上的二次曲线空间。在这种情况下，如果X包含某个线性子簇，则空间的维数可能大于期望的维数。本文证明了：对于C上的光滑Fano超曲面X，X中的二次曲线空间的不可约分支R，如果R的一般二次曲线所张成的2-平面不包含在X中，则R的维数等于期望维数.
R. Beheshti showed that for a smooth Fano hypersurface X of degree⩽ 8 over the complex number field C, the dimension of the space of lines lying in X is equal to the expected dimension. We study the space of conics on X. In this case, if X contains some linear subvariety, then the dimension of the space can be larger than the expected dimension. In this paper, we show that for a smooth Fano hypersurface X of degree⩽ 6 over C, and for an irreducible component R of the space of conics lying in X, if the 2-plane spanned by a general conic of R is not contained in X, then the dimension of R is equal to the expected dimension.