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1999•Communications in AlgebraRequires access

New asymptotics for the existence of plane curves with prescribed singularities

Christoph Lossen

Open publisher page 20 citations

Abstract

We study the classical problem of the existence of irreducible plane curves with given degree d and prescribed singularities of topological types S 1,…,S r- Our main results concern substantial improvements of the leading coefficients in the asymptotically optimal sufficient conditions for complex plane curves which were found in [GLS1]. We then transfer these results to real plane curves.

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What this paper is about

We study the classical problem of the existence of irreducible plane curves with given degree d and prescribed singularities of topological types S 1,…,S r- Our main results concern substantial improvements of the leading coefficients in the asymptotically optimal sufficient conditions for complex plane curves which were found in [GLS1]. We then transfer these results to real plane curves.

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OpenAlex reports 20 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We study the classical problem of the existence of irreducible plane curves with given degree d and prescribed singularities of topological types S 1,…,S r- Our main results concern substantial improvements of the leading coefficients in the asymptotically optimal sufficient conditions for complex plane curves which were found in [GLS1]. We then transfer these results to real plane curves.

Key concepts: Gravitational singularity, Mathematics, Plane curve, Plane (geometry), Degree (music), Complex plane, Mathematical analysis, Pure mathematics

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