The class of the locus of intermediate Jacobians of cubic threefolds
The class of the locus of intermediate Jacobians of cubic threefolds
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DOI：
10.1007/s00222-012-0377-4
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发表时间：
2011-03
影响因子：
3.1
通讯作者：
S. Grushevsky;K. Hulek
中科院分区：
文献类型：
--
作者：
S. Grushevsky;K. Hulek
本文研究了复主极化阿贝尔五重模空间中三次三重的中间Jacobian的轨迹，并将其推广到任意亏格上--θ因子上有奇异奇二扭点的阿贝尔簇的轨迹。假设这个位点具有期望的余维（我们证明对于g ≤5是正确的，对于任何g都是推测的），我们计算了这个轨迹的类，以及它在Chow、同调和重言环中的完美锥环形紧化中的闭包。我们详细计算了亏格直到5的情况，获得了in，和类的轨迹的中间雅可比（连同相同的轨迹的产品）。最后，我们得到了一些结果的轨迹的边界几何的三次三重的中间雅可比在我们的计算过程中，我们还处理各种交叉的边界因子的水平环面紧化，这是独立的兴趣，了解上同调和Chow环的模空间。
We study the locus of intermediate Jacobians of cubic threefolds within the moduli spaceof complex principally polarized abelian fivefolds, and its generalization to arbitrary genus—the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimensiong(which we show to be true forg≤5, and conjecturally for anyg), we compute the class of this locus, and of its closure in the perfect cone toroidal compactification, in the Chow, homology, and the tautological ring.We work out the cases of genus up to 5 in detail, obtaining explicit expressions for the class of the closure ofin, and for the class of the locus of intermediate Jacobians (together with the same locus of products)—in. Finally, we obtain some results on the geometry of the boundary of the locus of intermediate Jacobians of cubic threefolds in.In the course of our computation we also deal with various intersections of boundary divisors of a level toroidal compactification, which is of independent interest in understanding the cohomology and Chow rings of the moduli spaces.