Data di Pubblicazione:
2022
Citazione:
Characterizing some polarized Fano fibrations via Hilbert curves / A. Lanteri, A.L. Tironi. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - 21:3(2022 Mar), pp. 2250046.1-2250046.26. [10.1142/S0219498822500463]
Abstract:
The Hilbert curve of a complex polarized manifold (X,L) is the complex
affine plane curve of degree dim(X) defined by the Hilbert-like polynomial
chi(xK_X+yL), where K_X is the canonical bundle of X and x and y are regarded
as complex variables. A natural expectation is that this curve encodes several
properties of the pair (X,L). In particular, the existence of a fibration of X over a
variety of smaller dimension induced by a suitable adjoint bundle to L translates into
the fact that the Hilbert curve has a quite special shape. Along this line, Hilbert curves
of special varieties like Fano manifolds with low coindex, as well as fibrations over low
dimensional varieties having such a manifold as general fiber, endowed with
appropriate polarizations, are investigated. In particular, several polarized manifolds
relevant for adjunction theory are completely characterized in terms of their Hilbert curves.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
polarized manifold ; Hilbert curve, ;adjunction
Elenco autori:
A. Lanteri, A.L. Tironi
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