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Freeness versus maximal degree of the singular subscheme for surfaces in \(\mathbb {P}^3\)

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Abstract

We show that a free surface in \(\mathbb {P}^3\) is characterized by the maximality of the degree of its singular subscheme, in the presence of an additional tameness condition. This is similar to the characterization of free plane curves by the maximality of their global Tjurina number given by A. A. du Plessis and C.T.C. Wall. Simple characterizations of the nearly free tame surfaces are also given.

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Authors and Affiliations

  1. CNRS, LJAD, UMR 7351, University of Nice Sophia Antipolis, 06100, Nice, France

    Alexandru Dimca

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  1. Alexandru Dimca
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Correspondence to Alexandru Dimca.

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Partially supported by Institut Universitaire de France.

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Dimca, A. Freeness versus maximal degree of the singular subscheme for surfaces in \(\mathbb {P}^3\) . Geom Dedicata 183, 101–112 (2016). https://doi.org/10.1007/s10711-016-0148-2

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  • DOI: https://doi.org/10.1007/s10711-016-0148-2

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