论文标题
K3 [n]型的Hyper-Kahler品种的理性杂货异构体是代数
Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic
论文作者
论文摘要
令x和y成为紧凑的超卡勒歧管，将变形等效到k3表面的长度为n子化的希尔伯特方案。如果其产品XXY中的同一个同类类是一种分析对应关系，如果它属于Chern类别相干分析搁板产生的子类别。让F为Beauville-Bogomolov-Fujiki配对的第二个理性共同体的杂物等轴测图。我们证明F是由分析对应诱导的。我们此外，将F提升为分析对应关系F之间的总合理共同体，这是相对于Mukai配对的杂物等轴测图，并保留了签名的等级。当X和Y投影时，对应关系F和F为代数。
Let X and Y be compact hyper-Kahler manifolds deformation equivalence to the Hilbert scheme of length n subschemes of a K3 surface. A cohomology class in their product XxY is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let f be a Hodge isometry of their second rational cohomologies with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an analytic correspondence. We furthermore lift f to an analytic correspondence F between their total rational cohomologies, which is a Hodge isometry with respect to the Mukai pairings, and which preserves the gradings up to sign. When X and Y are projective the correspondences f and F are algebraic.
