AI 中文总结
该研究通过对奇异Z/2-Godeaux曲面的Z/2×Z/4覆盖计算出八个伪二次曲面的显式双典范模型，证明其两两非同构且刚性，得到首批非同源曲线乘积的伪二次曲面显式射影模型。
AI 中文摘要
我们计算了八个伪二次曲面的显式定义方程，这些伪二次曲面是由第二作者早期工作中得到的两个奇异Z/2-Godeaux曲面的Z/2×Z/4覆盖。从Godeaux曲面的通用覆盖的显式方程出发，我们重构了相关的特征特征空间，并确定了这八个伪二次曲面在P^8中的双典范模型的齐次理想。所有八个模型都定义在Q上。我们证明这些曲面两两非同构且刚性。结合早期工作中建立的非乘积结果，这给出了首批非同源曲线乘积的伪二次曲面的显式射影模型。
英文摘要
We compute explicit defining equations for eight fake quadrics arising as $\mathbb Z/2\times\mathbb Z/4$-covers of two singular $\mathbb Z/2$-Godeaux surfaces obtained in earlier work of the second author. Starting from explicit equations for the universal covers of the Godeaux surfaces, we reconstruct the relevant character eigenspaces and determine the homogeneous ideals of the bicanonical models of the eight fake quadrics in $\mathbb P^8$. All eight models are defined over $\mathbb Q$. We prove that the surfaces are pairwise non-isomorphic and rigid. Combined with the non-product result established in the earlier work, this gives the first explicit projective models of fake quadrics which are not isogenous to a product of curves.
