Let (X,L) be a quadric fibration over a smooth curve. The explicit equation of the corresponding Hilbert curve \Gamma is obtained. The geometry of \Gamma reflects some structure properties of (X,L); in particular, its special shape allows us to recognize that (X,L) is a quadric fibration. In fact \Gamma is reducible into \dim X -2 parallel lines with prescribed slope, evenly spaced, plus a conic. On the other hand, this conic can itself be regarded as the Hilbert curve of a polarized surface only in very rare circumstances.
Hilbert curves of quadric fibrations / A. Lanteri. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 29:10(2018 Oct). [10.1142/S0129167X18500672]
Hilbert curves of quadric fibrations
A. Lanteri
2018
Abstract
Let (X,L) be a quadric fibration over a smooth curve. The explicit equation of the corresponding Hilbert curve \Gamma is obtained. The geometry of \Gamma reflects some structure properties of (X,L); in particular, its special shape allows us to recognize that (X,L) is a quadric fibration. In fact \Gamma is reducible into \dim X -2 parallel lines with prescribed slope, evenly spaced, plus a conic. On the other hand, this conic can itself be regarded as the Hilbert curve of a polarized surface only in very rare circumstances.File | Dimensione | Formato | |
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