For infinitely many d, Hassett showed that special cubic fourfolds of discriminant d are related to polarised K3 surfaces of degree d via their Hodge structures. For half of the d, each associated K3 surface (S, L) canonically yields another one, (Sτ, Lτ). We prove that Sτ is isomorphic to the moduli space of stable coherent sheaves on S with Mukai vector (3, L, d/6). We also explain for which d the Hilbert schemes Hilbn (S) and Hilbn (Sτ) are birational.

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两个极化 K3 表面与同一个立方四倍相关联

对于无限多d, Hassett 证明了特殊的三次四倍判别式d与度数的偏振 K3 表面有关d通过他们的霍奇结构。对于一半d, 每个关联的 K3 曲面 (小号,大号) 典型地产生另一个， (小号τ,大号τ）。我们证明小号τ同构于稳定连贯滑轮的模空间小号用 Mukai 向量 (3,大号,d/6)。我们还解释了d希尔伯特方案 Hilbn(小号) 和希尔布n(小号τ) 是双理性的。