AI 中文总结
研究特征为0的代数闭域上具有简单雅可比矩阵的光滑射影连通曲线的自同构群，通过构造曲线族并证明其密度为1的成员集有简单雅可比矩阵，在主极化阿贝尔簇模空间中给出无限多个新的不太可能的交的例子。
AI 中文摘要
我们对特征为0的代数闭域上具有简单雅可比矩阵的光滑、射影、连通曲线的所有自同构群进行分类。对于该分类中的每个非平凡群，我们构造了一族具有该自同构群的曲线，并证明密度为1的成员集具有简单雅可比矩阵。这些族在主极化阿贝尔簇的模空间中产生了无限多个新的不太可能的交的例子。
英文摘要
We classify all automorphism groups of smooth, projective, connected curves over an algebraically closed field of characteristic $0$ with simple Jacobians. For every nontrivial group in this classification, we construct a family of curves with that automorphism group and prove that a density-one set of members has simple Jacobian. These families yield infinitely many new examples of unlikely intersections in the moduli spaces of principally polarized abelian varieties.
Comments44 pages, comments are very welcome
