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arXiv · 1610.08140

Extended Klein model and a bound on curves with negative self-intersection

Xin Xiong
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Abstract

Let $S$ be an irreducible smooth projective surface and $\mathcal{F}$ a collection of curves with negative self-intersection on $S$ such that no positive combination $aC_1 + bC_2$ is connected nef. In this paper, we provide an alternate proof that $\mathcal{F}$ is bounded by an exponential function of the Picard number $\rho(S)$ of $S$ using an extended version of the Klein disc model for hyperbolic space.

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Xin Xiong. 2016-10-26. Extended Klein model and a bound on curves with negative self-intersection. https://arxiv.org/abs/1610.08140

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