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arXiv · 1408.0190

On the self-intersection number of the nonsingular models of rational cuspidal plane curves

Keita Tono
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Abstract

In this paper, we consider rational cuspidal plane curves having at least three cusps. We give an upper bound of the self-intersection number of the proper transforms of such curves via the minimal embedded resolution of the cusps. For a curve having exactly three cusps, we show that the self-intersection number is equal to the bound if and only if the curve coincides with the quartic curve having three cusps.

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Keita Tono. 2014-08-01. On the self-intersection number of the nonsingular models of rational cuspidal plane curves. https://arxiv.org/abs/1408.0190

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