Given a smooth complex projective variety X and an ample line bundle L on it, one can associate the Hilbert curve with (X,L). This is a plane affine algebraic curve, whose equation depends only on the numerical characters of X and L. In particular, two numerically equivalent ample line bundles on X lead to the sameHilbert curve. Focusing on the case of surfaces, in this paper we investigate how far the converse is from being true.
HC-equivalence vs numerical equivalence for ample line bundles on surfaces / A. Lanteri. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - II Serie, vol. 66(2017 Apr), pp. 113-123.
HC-equivalence vs numerical equivalence for ample line bundles on surfaces
A. Lanteri
2017
Abstract
Given a smooth complex projective variety X and an ample line bundle L on it, one can associate the Hilbert curve with (X,L). This is a plane affine algebraic curve, whose equation depends only on the numerical characters of X and L. In particular, two numerically equivalent ample line bundles on X lead to the sameHilbert curve. Focusing on the case of surfaces, in this paper we investigate how far the converse is from being true.
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