AI 中文总结
该研究构造了一个特殊的典范极化三维簇，其归一化凯勒-爱因斯坦度量存在不可积的无穷小爱因斯坦形变，回答了Dai等人提出的相关推广问题。
AI 中文摘要
我们构造了一个光滑的典范极化三维簇，它不与正维数簇的乘积全纯同构，其归一化凯勒-爱因斯坦度量允许一个不可积的无穷小爱因斯坦形变；该切方向作为无穷小复形变也是不可积的。事实上，该例子中无穷小爱因斯坦形变空间的实维数为8，其可积方向构成一个实6维子空间，该子空间外的每个方向均是受阻的。这回答了Dai、Wang和Wei提出的实维数6问题的适当推广版本的两部分。
英文摘要
We construct a smooth canonically polarized threefold, not biholomorphic to a product of positive-dimensional varieties, whose normalized Kähler-Einstein metric admits a non-integrable infinitesimal Einstein deformation. The same tangent direction is non-integrable as an infinitesimal complex deformation. In fact, the space of infinitesimal Einstein deformations in our example has real dimension 8, its integrable directions form a real 6-dimensional subspace, and every direction outside that subspace is obstructed. This answers both parts of a suitably generalized version of a question posed by Dai, Wang, and Wei in real dimension 6.
