论文标题
在霍奇基因座
On a Hodge locus
论文作者
论文摘要
在许多情况下，代数循环的同源性类别的变形空间作为hodge循环大于其变形空间作为代数循环。这种现象可能会发生在高空曲面中的代数周期中，但是，我们只能通过计算机实验来为其收集证据。在本文中，我们将其描述为Cutichyperfaces的一个例子。在这种情况下，提出了上述现象的验证是第一个GADEPS问题。主要目标是在这种情况下验证（变异）霍奇猜想，或者收集证据表明它可能会引起霍奇猜想的反例。
There are many instances such that deformation space of the homology class of an algebraic cycle as a Hodge cycle is larger than its deformation space as algebraic cycle. This phenomena can occur for algebraic cycles inside hypersurfaces, however, we are only able to gather evidences for it by computer experiments. In this article we describe one example of this for cubic hypersurfaces. The verification of the mentioned phenomena in this case is proposed as the first GADEPs problem. The main goal is either to verify the (variational) Hodge conjecture in such a case or gather evidences that it might produce a counterexample to the Hodge conjecture.
