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arXiv · 2404.09208

Logarithmic multicanonical systems of smooth affine surfaces of logarithmic Kodaira dimension one

Hideo Kojima
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Abstract

Let $S$ be a smooth affine surface of logarithmic Kodaira dimension one and let $(V,D)$ be a pair of a smooth projective surface $V$ and a simple normal crossing divisor $D$ on $V$ such that $V \setminus \operatorname{Supp} D = S$. In this paper, we consider the logarithmic multicanonical system $|m(K_V + D)|$. We prove that, for any $m \geq 8$, $|m(K_V+D)|$ gives an $\mathbb{P}^1$-fibration form $V$ onto a smooth projective curve.

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Hideo Kojima. 2024-04-14. Logarithmic multicanonical systems of smooth affine surfaces of logarithmic Kodaira dimension one. https://arxiv.org/abs/2404.09208

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