论文标题
Beauville-Mukai Systems III的生育几何学：渐近行为
Birational geometry of Beauville-Mukai systems III: asymptotic behavior
论文作者
论文摘要
假设PICARD等级的K3表面上的Hilbert方案承认了理性的Lagrangian纤维化。我们表明，如果与点的数量相比，表面的程度足够大，那么希尔伯特方案是其Birational类中独特的Hyperkähler歧管。特别是，希尔伯特方案是一种拉格朗日纤维化本身，我们意识到，它来自S. S.的傅立叶 - 穆凯系统（扭曲的）Beauville-Mukai系统。我们还表明，当表面的程度很小时，我们的方法可用于找到Hilbert方案的所有Bibational模型。
Suppose that a Hilbert scheme of points on a K3 surface S of Picard rank one admits a rational Lagrangian fibration. We show that if the degree of the surface is sufficiently large compared to the number of points, then the Hilbert scheme is the unique hyperkähler manifold in its birational class. In particular, the Hilbert scheme is a Lagrangian fibration itself, which we realize as coming from a (twisted) Beauville-Mukai system on a Fourier-Mukai partner of S. We also show that when the degree of the surface is small our method can be used to find all birational models of the Hilbert scheme.
