Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908643539025920 |
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| author | Cho, Gunhee Cho, Myungsin |
| author_facet | Cho, Gunhee Cho, Myungsin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds Cho, Gunhee Cho, Myungsin Algebraic Geometry Complex Variables 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. |
| title | Structural Invariance of Green--Griffiths--Demailly Thresholds on Compact Complex Orbifolds |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2511.05830 |