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

Author:

Takayuki Koike

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-07-20 16:00:00

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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