紧致复轨道上Green-Griffiths-Demaily拓扑的结构不变性
Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds
摘要：
我们证明了格林-格里菲斯-Demailly（GGD）双曲阈值是结构不变的。换句话说，当从一个紧致的复流形到任何具有相同粗Kähler类的紧致光滑解析Deligne-Mumford堆栈（orbifold）时，不变喷流微分出现的最小喷流阶数和渐近增长率保持不变。我们建立了一个orbifold Riemann-Roch公式，表明只有身份部门有助于领导的$m^n$项的欧拉示性数$χ$，而所有扭曲的部门只贡献$O(m^{n-1})$。再加上曲率-正属性的Demailly-森普尔塔，这意味着不变的喷流微分的存在范围仅取决于粗凯勒类-因此orbifold紧化或刚化不改变GGD阈值或双曲轨迹。
英文摘要：
We prove that the Green--Griffiths--Demailly (GGD) hyperbolicity thresholds are structurally invariant. In other words, the minimal jet order and asymptotic growth rate at which invariant jet differentials appear remain unchanged when passing from a compact complex manifold to any compact smooth analytic Deligne--Mumford stack (orbifold) with the same coarse Kähler class. We establish an orbifold Riemann--Roch formula showing that only the identity sector contributes to the leading $m^n$ term of the Euler characteristic $χ$, while all twisted sectors contribute only $O(m^{n-1})$. Together with curvature--positivity properties of the Demailly--Semple tower, this implies that the existence range of invariant jet differentials depends solely on the coarse Kähler class--hence orbifold compactification or rigidification does not alter the GGD threshold or the hyperbolicity locus.
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