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HC-equivalence vs numerical equivalence for ample line bundles on surfaces

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Abstract

Given a smooth complex projective variety X and an ample line bundle \(\mathcal{L}\) on it, one can associate the Hilbert curve with \((X,\mathcal{L})\). This is a plane affine algebraic curve, whose equation depends only on the numerical characters of X and \(\mathcal{L}\). In particular, two numerically equivalent ample line bundles on X lead to the same Hilbert curve. Focusing on the case of surfaces, in this paper we investigate how far the converse is from being true.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini 50, 20133, Milano, Italy

    Antonio Lanteri

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  1. Antonio Lanteri
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Correspondence to Antonio Lanteri.

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

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Lanteri, A. HC-equivalence vs numerical equivalence for ample line bundles on surfaces. Rend. Circ. Mat. Palermo, II. Ser 66, 113–123 (2017). https://doi.org/10.1007/s12215-016-0271-9

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  • DOI: https://doi.org/10.1007/s12215-016-0271-9

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