Twisted cubics on singular cubic fourfolds—On Starr’s fibration
Twisted cubics on singular cubic fourfolds—On Starr’s fibration
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DOI：
10.1007/s00209-017-2021-x
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发表时间：
2015-04
影响因子：
0.8
通讯作者：
C. Lehn
中科院分区：
文献类型：
--
作者：
C. Lehn
我们证明了在不含平面的三次超曲面上的三次扭曲三次曲面上Starr纤维的全空间的Hilbert格式紧化允许收缩到八维奇异射影辛簇，它具有相当于光滑三次曲面上的扭曲三次曲面构造的八重辛的锐化分辨率变形.这又证明了K3曲面上四点的八重辛格式和Hilbert格式是形变等价的。作为一个副产品，我们对奇异三次四重曲线上的各种直线得到了类似的结果。
We show that the Hilbert scheme compactification of the total space of Starr’s fibration on the space of twisted cubics on a cubic hypersurface innot containing a plane admits a contraction to a singular projective symplectic variety of dimension eight which has a crepant resolution deformation equivalent to the symplectic eightfold constructed from twisted cubics on a smooth cubic fourfold. This yields another proof that the symplectic eightfold and the Hilbert scheme of four points on a K3 surface are deformation equivalent. As a byproduct we obtain similar results for the variety of lines on a singular cubic fourfold.