论文标题
对称力量的双曲和特殊性
Hyperbolicity and Specialness of Symmetric Powers
论文作者
论文摘要
受到Arapura和Archava的复杂投影量X的对称能力XM的Kodaira尺寸的计算，我们研究了它们的分析和代数双曲线特性。首先，我们显示XM是特殊的，并且仅在X是特殊时（当X的核心为曲线时）。然后，我们在K3表面的（suf-Fiper-Hig）对称能力和曲线产物中构建密集的整个曲线。我们还基于喷气差束的阳性给出标准，这意味着对称能力的伪用力。作为一种应用，我们获得了足够高的通用投射超壁面的对称能力的Kobayashi双曲线。在代数方面，我们给出一个标准，暗示着Codimension $ \ le $ n -2的对称力量的子变量是一般类型。这特别适用于具有足够的cotangent束的品种。最后，基于公制方法，我们研究球人的对称能力。
Inspired by the computation of the Kodaira dimension of symmetric powers Xm of a complex projective variety X of dimension n $\ge$ 2 by Arapura and Archava, we study their analytic and algebraic hyperbolic properties. First we show that Xm is special if and only if X is special (except when the core of X is a curve). Then we construct dense entire curves in (suf-ficiently hig) symmetric powers of K3 surfaces and product of curves. We also give a criterion based on the positivity of jet differentials bundles that implies pseudo-hyperbolicity of symmetric powers. As an application, we obtain the Kobayashi hyperbolicity of symmetric powers of generic projective hypersur-faces of sufficiently high degree. On the algebraic side, we give a criterion implying that subvarieties of codimension $\le$ n -- 2 of symmetric powers are of general type. This applies in particular to varieties with ample cotangent bundles. Finally, based on a metric approach we study symmetric powers of ball quotients.
