Nihonkai Mathematical Journal

Rational unicuspidal curves on $\mathbb Q$-homology projective planes whose complements have logarithmic Kodaira dimension $-\infty$

Hideo Kojima

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Abstract

Let $S$ be a $\mathbb Q$-homology projective plane, $C$ a rational unicuspidal curve on $S^0 = S - \operatorname{Sing} S$ and $C'$ the proper transform of $C$ with respect to the minimal embedded resolution of $C$. We prove that $S^0 - C$ is affine ruled if and only if $C'^2 \geq -1$ and determine the pairs $(S,C)$ when $\overline{\kappa}(S^0 -C) = -\infty$ and $C'^2 \leq -2$.

Note

This work was supported by JSPS KAKENHI Grant Number JP17K05198.

Note

The author would like to express his gratitude to the referee for giving useful comments and suggestions to improve the paper.

Article information

Source
Nihonkai Math. J., Volume 29, Number 1 (2018), 29-43.

Dates
Received: 11 June 2017
Revised: 9 October 2017
First available in Project Euclid: 6 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1549422082

Mathematical Reviews number (MathSciNet)
MR3908817

Zentralblatt MATH identifier
07063839

Subjects
Primary: 14J26: Rational and ruled surfaces
Secondary: 14J17: Singularities [See also 14B05, 14E15]

Keywords
rational cuspidal curve $\mathbb Q$-homology projective plane

Citation

Kojima, Hideo. Rational unicuspidal curves on $\mathbb Q$-homology projective planes whose complements have logarithmic Kodaira dimension $-\infty$. Nihonkai Math. J. 29 (2018), no. 1, 29--43. https://projecteuclid.org/euclid.nihmj/1549422082


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