In dimension n = 2m − 2 ≥ 4 adjunction theoretic scrolls over a smooth mfold may not be classical scrolls, due to the existence of divisorial fibers. A 4-dimensional scroll (X, L) over P 3 of this type is considered, and the equation of its Hilbert curve Γ is determined in two ways, one of which relies on the fact that (X, L) is at the same time a classical scroll over a threefold Y 6= P 3 . It turns out that Γ does not perceive divisorial fibers. The equation we obtain also shows that a question raised in [4] has negative answer in general for non-classical scrolls over a 3-fold. More precisely, the answer for (X, L) is negative or positive according to whether (X, L) is regarded as an adjunction theoretic scroll or as a classical scroll; in other words, it is the answer to this question to distinguish between the existence of jumping fibers or not.

The Hilbert curve of a 4-dimensional scroll with a divisorial fiber / A. Lanteri, A.L. Tironi. - In: TAIWANESE JOURNAL OF MATHEMATICS. - ISSN 1027-5487. - 24:1(2020 Feb), pp. 31-41. [10.11650/tjm/190206]

The Hilbert curve of a 4-dimensional scroll with a divisorial fiber

A. Lanteri
;
A.L. Tironi
2020

Abstract

In dimension n = 2m − 2 ≥ 4 adjunction theoretic scrolls over a smooth mfold may not be classical scrolls, due to the existence of divisorial fibers. A 4-dimensional scroll (X, L) over P 3 of this type is considered, and the equation of its Hilbert curve Γ is determined in two ways, one of which relies on the fact that (X, L) is at the same time a classical scroll over a threefold Y 6= P 3 . It turns out that Γ does not perceive divisorial fibers. The equation we obtain also shows that a question raised in [4] has negative answer in general for non-classical scrolls over a 3-fold. More precisely, the answer for (X, L) is negative or positive according to whether (X, L) is regarded as an adjunction theoretic scroll or as a classical scroll; in other words, it is the answer to this question to distinguish between the existence of jumping fibers or not.
English
scroll; divisorial fiber; Hilbert curve
Settore MAT/03 - Geometria
Articolo
Esperti anonimi
Ricerca di base
Pubblicazione scientifica
   Geometry of Algebraic Varieties
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   2015EYPTSB_006
feb-2020
12-mar-2019
Mathematical Society of the Republic of China
24
1
31
41
11
Pubblicato
Periodico con rilevanza internazionale
Aderisco
info:eu-repo/semantics/article
The Hilbert curve of a 4-dimensional scroll with a divisorial fiber / A. Lanteri, A.L. Tironi. - In: TAIWANESE JOURNAL OF MATHEMATICS. - ISSN 1027-5487. - 24:1(2020 Feb), pp. 31-41. [10.11650/tjm/190206]
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Article (author)
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A. Lanteri, A.L. Tironi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/662542
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