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Plane curves of minimal degree with prescribed singularities

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Inventiones mathematicae Aims and scope

Abstract.

We prove that there exists a positive α such that for any integer d≥3 and any topological types S 1,…,S n of plane curve singularities, satisfying

there exists a reduced irreducible plane curve of degree d with exactly n singular points of types S 1,…,S n , respectively. This estimate is optimal with respect to the exponent of d. In particular, we prove that for any topological type S there exists an irreducible polynomial of degree having a singular point of type S.

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Oblatum 20-VI-1996 & 11-III-1997

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Greuel, GM., Lossen, C. & Shustin, E. Plane curves of minimal degree with prescribed singularities. Invent math 133, 539–580 (1998). https://doi.org/10.1007/s002220050254

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  • DOI: https://doi.org/10.1007/s002220050254

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