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Canonical surfaces of higher degree

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Abstract

We consider a family of surfaces of general type S with \(K_S\) ample, having \(K^2_S = 24, p_g (S) = 6, q(S)=0\). We prove that for these surfaces the canonical system is base point free and yields an embedding \(\Phi _1 : S \rightarrow \mathbb {P}^5\). This result answers a question posed by Kapustka and Kapustka (Bilinkage in codimension 3 and canonical surfaces of degree 18 in \({\mathbb {P}}^5\). arXiv:1312.2824, 2015). We discuss some related open problems, concerning also the case \(p_g(S) = 5\), where one requires the canonical map to be birational onto its image.

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Notes

  1. This follows from theorem 3.8 of [3].

  2. For which however we have not yet found a reference.

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Acknowledgments

Funding was provided by European Research Council (Grant No. 340258).

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Authors and Affiliations

  1. Lehrstuhl Mathematik VIII, Mathematisches Institut der Universität Bayreuth, NW II, Universitätsstr. 30, 95447, Bayreuth, Germany

    Fabrizio Catanese

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  1. Fabrizio Catanese
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Correspondence to Fabrizio Catanese.

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Dedicated to Philippe Ellia on the occasion of his 60th birthday.

The present work took place in the realm of the ERC Advanced Grant No. 340258, ‘TADMICAMT’.

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Catanese, F. Canonical surfaces of higher degree. Rend. Circ. Mat. Palermo, II. Ser 66, 43–51 (2017). https://doi.org/10.1007/s12215-016-0274-6

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  • DOI: https://doi.org/10.1007/s12215-016-0274-6

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