论文标题
合理的立方四倍，具有相关的奇异K3表面
Rational cubic fourfolds with associated singular K3 surfaces
论文作者
论文摘要
概括了最近的杨和Yu结构，我们研究了一个人可以在多大程度上与Hassett的Noether-Lefschetz Divisors交流$ \ Mathcal {C} _d $在立方四倍$ \ MATHCAL {C C} $的Moduli空间中。特别是，我们在20个索引上表现出算术条件$ d_1，\ dots，d_ {20} $，以确保除数$ \ nathcal {c} _ {c} _ {d_1}，\ dots，\ mathcal {c} _ {c} _ {d _ {d_ {20}}} $另一个。这使我们能够生成具有与秩20néron-severi组相关的K3表面的理性立方四倍的示例，即单数K3表面。
Generalizing a recent construction of Yang and Yu, we study to what extent one can intersect Hassett's Noether-Lefschetz divisors $\mathcal{C}_d$ in the moduli space of cubic fourfolds $\mathcal{C}$. In particular, we exhibit arithmetic conditions on 20 indexes $d_1,\dots, d_{20}$ that assure that the divisors $\mathcal{C}_{d_1},\dots,\mathcal{C}_{d_{20}}$ all intersect one another. This allows us to produce examples of rational cubic fourfolds with an associated K3 surface with rank 20 Néron-Severi group, i.e. a singular K3 surface.
