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On a conjecture on the variety of lines on Fano complete intersections
Annali di Matematica Pura ed Applicata ( IF 1.0 ) Pub Date : 2021-03-03 , DOI: 10.1007/s10231-021-01071-z
Samir Canning

The Debarre-de Jong conjecture predicts that the Fano variety of lines on a smooth Fano hypersurface in \(\mathbb {P}^n\) is always of the expected dimension. We generalize this conjecture to the case of smooth Fano complete intersections and prove that for a smooth Fano complete intersection \(X\subset \mathbb {P}^n\) of hypersurfaces whose degrees sum to at most 7, the Fano variety of lines on X has the expected dimension.



中文翻译:

关于法诺完整交集上各种线的猜想

Debarre-de Jong猜想预测\(\ mathbb {P} ^ n \)中的光滑Fano超曲面上的Fano线总是具有预期的尺寸。我们将该猜想推广到光滑Fano完整交点的情况,并证明对于度数最大为7的超曲面的光滑Fano完整交点\(X \ subset \ mathbb {P} ^ n \),Fano各种线在X上具有预期的尺寸。

更新日期:2021-03-04
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