Data di Pubblicazione:
2023
Citazione:
Hilbert curves of scrolls over threefolds / M.L. Fania, A. Lanteri. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 227:10(2023), pp. 107380.1-107380.20. [10.1016/j.jpaa.2023.107380]
Abstract:
Let (X,L) be a complex polarized n-fold with the structure of a classical scroll over a smooth projective threefold Y. The Hilbert curve of such a pair (X,L) is a complex affine plane curve of degree n, consisting of n−3 evenly spaced parallel lines plus a cubic. This paper is devoted to a detailed study of this cubic. In particular, existence of triple points, behavior with respect to the line at infinity, and non-reducedness, are analyzed in connection with the structure of (X,L). Special attention is reserved to the case n=4, where various examples are presented and the possibility that the cubic is itself the Hilbert curve of the base threefold Y for a suitable polarization is discussed.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hilbert curve; Scroll; Vector bundle
Elenco autori:
M.L. Fania, A. Lanteri
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