Let (X,L) be a polarized manifold of dimension n. Its Hilbert curve is an affine algebraic plane curve of degree n encoding properties related to fibrations of X, defined by suitable adjoint linear systems to L. In particular, if (X,L) is a scroll over a smooth surface S, its Hilbert curve consists of n−2 parallel lines with a given slope and evenly spaced, plus a conic. Making its equation explicit, we show that this conic turns out to be itself the Hilbert curve of the ℚ-polarized surface (Formula presented.), where ℰ is the rank-(n−1) vector bundle obtained by pushing down L via the scroll projection, if and only if ℰ is properly semistable in the sense of Bogomolov.
Titolo: | A property of Hilbert curves of scrolls over surfaces |
Autori: | |
Parole Chiave: | Hilbert curve; scroll; vector bundle (properly semistable); Q-polarized surface |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Data di pubblicazione: | 2018 |
Rivista: | |
Tipologia: | Article (author) |
Data ahead of print / Data di stampa: | 2-mag-2018 |
Digital Object Identifier (DOI): | 10.1080/00927872.2018.1464169 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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