Corollary 19.9.24`D22F138F2F08`

Corollary 19.9.24.D22F138F2F08 If $\dim X=2$, then $h^ q(X,L^ p\otimes E)=O(p^ r)$ for every fixed holomorphic vector bundle $E$ and $0\leq q\leq 2$.

Proof. The endpoints have already been bounded. Since $\chi =h^0-h^1+h^2$, the middle dimension is at most $h^0+h^2+|\chi |=O(p^ r)$ by the Euler polynomial. $\square$

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BibTeX citation

@misc{pome-tag-D22F138F2F08,
  author = {{Pome contributors}},
  title = {Corollary 19.9.24},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/D22F138F2F08/}
}

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Corollary 19.9.24D22F138F2F08

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Corollary 19.9.24`D22F138F2F08`