Data di Pubblicazione:
2021
Citazione:
On the structure of generalized polarized manifolds with relatively small second class / A. Lanteri, A.L. Tironi. - In: TOKYO JOURNAL OF MATHEMATICS. - ISSN 0387-3870. - 44:2(2021 Dec), pp. 417-438. [10.3836/tjm/1502179348]
Abstract:
Let X be a smooth complex projective variety of dimension n geq 2 polarized by an ample line bundle H.
For n=2, the structure of pairs (X,H) as above is described under the assumption that m-3d leq 4, where m
and d stand for the class and the degree of (X,H), respectively.
In particular, special attention is payed to the case m-2d leq 1, in which X turns out to be a ruled surface.
In higher dimensions, adding to the above setting an ample vector bundle E of rank r leq n-2 on X such that
F:=E oplus H^{oplus n-r-2} admits a regular section vanishing on a smooth surface, by relying on the analysis
made in the surface case, the structure of the generalized polarized manifold (X,mathcal F) is described
for small values of m_2 - 3d, where m_2:=m_2(X,E,H) is the generalized second class defined in a previous
paper and d:=c_{n-2}(F) H^2.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Ample vector bundle; special variety; surface:
Elenco autori:
A. Lanteri, A.L. Tironi
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