Data di Pubblicazione:
2018
Citazione:
A property of Hilbert curves of scrolls over surfaces / A. Lanteri. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - (2018). [Epub ahead of print] [10.1080/00927872.2018.1464169]
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hilbert curve; scroll; vector bundle (properly semistable); Q-polarized surface
Elenco autori:
A. Lanteri
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