论文标题
特征叶 - 调查
Characteristic foliations -- a survey
论文作者
论文摘要
这是一篇调查文章，基本上是完整的证据，表明了一系列有关紧凑型Hyperkähler歧管中平滑除数的特征性叶片的几何形状，从Hwang-Viehweg的工作开始，但也涵盖了Amerik-Campana和Abugaliv的文章。 Hyperkähler歧管上的全态符号形式的限制限制对平滑性超表面$ d \ subset x $的限制会导致常规叶面$ {\ Mathcal f} \ subset {\ Mathcal T} _d n级，等级一，有特色的叶子。图片在第四维度中完成，并表明$ d $上的$ {\ Mathcal f} $的叶子的行为由Beauville-Bogomolov Square $ Q（d）$ $ d $确定。在较高的维度中，某些结果取决于$ d $的丰度猜想。
This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperkähler manifolds, starting with work by Hwang-Viehweg, but also covering articles by Amerik-Campana and Abugaliev. The restriction of the holomorphic symplectic form on a hyperkähler manifold $X$ to a smooth hypersurface $D\subset X$ leads to a regular foliation ${\mathcal F}\subset{\mathcal T}_D$ of rank one, the characteristic foliation. The picture is complete in dimension four and shows that the behavior of the leaves of ${\mathcal F}$ on $D$ is determined by the Beauville-Bogomolov square $q(D)$ of $D$. In higher dimensions, some of the results depend on the abundance conjecture for $D$.
