arXiv subjects

Keita Tono

Publications and source records attributed to Keita Tono.

5 recordsLinked to original sources

arXiv2014

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

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.

math.AG↗

arXiv2012

On a new class of rational cuspidal plane curves with two cusps

In this paper, we consider rational cuspidal plane curves having exactly two cusps 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 cusps have maximal self-intersection number.

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arXiv2009

On Orevkov's rational cuspidal plane curves

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.

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arXiv2009

The projective characterization of elliptic plane curves which have one place at infinity

In this paper we consider smooth affine elliptic plane curves having one place at infinity. We identify them with elliptic projective plane curves having only one cusp as their singular points and meeting with the line at infinity only at the cusp. We characterize such curves by the self-intersection number of the strict transform of them via the minimal embedded resolution of their cusp. Furthermore, we prove that the self-intersection number of them is the maximum value among those of all the elliptic plane curves having only one cusp.

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arXiv2008

Hyperelliptic plane curves of type (d,d-2)

In a previous paper, we classified and constructed all rational plane curves of type (d,d-2). In this paper, we generalize these results to irreducible plane curves of type (d,d-2) with positive genus.

math.AG↗