$\overline{\partial}$ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface

Takayuki Koike

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arXiv · 2308.03761

$\overline{\partial}$ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface

Takayuki Koike

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Abstract

Let $X$ be a non-singular compact complex surface such that the anticanonical line bundle admits a smooth Hermitian metric with semi-positive curvature. For a non-singular hypersurface $Y$ which defines an anticanonical divisor, we investigate the $\overline{\partial}$ cohomology group $H^1(M, \mathcal{O}_M)$ of the complement $M=X\setminus Y$.

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Takayuki Koike. 2023-07-21. $\overline{\partial}$ cohomology of the complement of a semi-positive anticanonical divisor of a compact surface. https://arxiv.org/abs/2308.03761

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