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

2014/08/01 by Keita Tono, Tono, Keita
Mathematics · #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H50

paper · pdf · doi:10.48550/arxiv.1408.0190

17 pages

arxiv created 2014/08/01 · arxiv updated 2014/08/04

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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