论文标题
立方四倍，有所
Cubic Fourfolds with an Involution
论文作者
论文摘要
立方四倍有三种类型。两种抗糖质类型和一种符号。在这里，我们表明，与理性猜想有关的立方体表现出与理性猜想有关的全部行为。也就是说，我们显示出具有符号相关性的一般立方四倍，没有相关的K3表面，并且是不合理的。相比之下，我们显示了一个具有特定抗糖反应的立方四倍，具有相关的K3，实际上是理性的。我们表明，这种立方体包含在所有非空哈塞特分隔线的交集中；我们称这种立方体哈塞特最大。我们在理论和几何上研究了晶格的代数和先验晶格的代数和先验晶格。
There are three types of involutions on a cubic fourfold; two of anti-symplectic type, and one symplectic. Here we show that cubics with involutions exhibit the full range of behaviour in relation to rationality conjectures. Namely, we show a general cubic fourfold with symplectic involution has no associated K3 surface and is conjecturely irrational. In contrast, we show a cubic fourfold with a particular anti-symplectic involution has an associated K3, and is in fact rational. We show such a cubic is contained in the intersection of all non-empty Hassett divisors; we call such a cubic Hassett maximal. We study the algebraic and transcendental lattices for cubics with an involution both lattice theoretically and geometrically.
