Let X be a projective bundle over a smooth curve and let L be an ample line bundle on X inducing O_{\mathbb P}(r) on every fiber. The Hilbert curve \Gamma of such a polarized manifold (X,L) is explicitly described and the reconstruction problem is addressed. In particular, it is shown that the very special geographic shape of \Gamma allows to recover the adjunction theoretic type of (X,L) for smooth surfaces, for scrolls over a smooth curve, as well as for Veronese bundles under additional assumptions.

Characterizing scrolls via the Hilbert curve / A. Lanteri. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 25:11(2014 Nov), pp. 1450101.1-1450101.17. [10.1142/S0129167X14501018]

Characterizing scrolls via the Hilbert curve

A. Lanteri
2014

Abstract

Let X be a projective bundle over a smooth curve and let L be an ample line bundle on X inducing O_{\mathbb P}(r) on every fiber. The Hilbert curve \Gamma of such a polarized manifold (X,L) is explicitly described and the reconstruction problem is addressed. In particular, it is shown that the very special geographic shape of \Gamma allows to recover the adjunction theoretic type of (X,L) for smooth surfaces, for scrolls over a smooth curve, as well as for Veronese bundles under additional assumptions.
Polarized manifold; Hilbert curve; Projective bundle; Scroll
Settore MAT/03 - Geometria
nov-2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/251037
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