Journal of the Mathematical Society of Japan

On Orevkov's rational cuspidal plane curves

Keita TONO

Abstract

In this note, we consider rational cuspidal plane curves having exactly one cusp whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal embedded resolution of the cusp have the maximal self-intersection number. We show that the curves given by the classification coincide with those constructed by Orevkov.

Article information

Source
J. Math. Soc. Japan, Volume 64, Number 2 (2012), 365-385.

Dates
First available in Project Euclid: 26 April 2012

https://projecteuclid.org/euclid.jmsj/1335444396

Digital Object Identifier
doi:10.2969/jmsj/06420365

Mathematical Reviews number (MathSciNet)
MR2916072

Zentralblatt MATH identifier
1246.14044

Subjects
Primary: 14H50: Plane and space curves

Keywords
rational plane curve cusp Orevkov

Citation

TONO, Keita. On Orevkov's rational cuspidal plane curves. J. Math. Soc. Japan 64 (2012), no. 2, 365--385. doi:10.2969/jmsj/06420365. https://projecteuclid.org/euclid.jmsj/1335444396

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