On a smooth complex projective variety X of dimension n, consider an ample vector bundle E of rank ran geq 2 and an ample line bundle H. A numerical character m_2 =m_2(X,E,H) of the triplet (X,E,H) is defined, extending the well-known second class of a polarized manifold (X,H), when either n = 2 or H is very ample. Under some additional assumptions on F : = E oplus H^{oplus (n-r-2)}, triplets (X,E,H) as above whose m_2 is small with respect to the invariants d := c_{n-2}(F) H^2 and g := 1 + (1/2)(K_X+c_1(F)+H) cdot c_{n-2}(F) cdot H are studied and classified.

Generalized polarized manifolds with low second class / A. Lanteri, A.L. Tironi. - In: HIROSHIMA MATHEMATICAL JOURNAL. - ISSN 0018-2079. - 51:3(2021 Nov), pp. 301-334. [10.32917/h2020070]

Generalized polarized manifolds with low second class

A. Lanteri
Primo
;
2021

Abstract

On a smooth complex projective variety X of dimension n, consider an ample vector bundle E of rank ran geq 2 and an ample line bundle H. A numerical character m_2 =m_2(X,E,H) of the triplet (X,E,H) is defined, extending the well-known second class of a polarized manifold (X,H), when either n = 2 or H is very ample. Under some additional assumptions on F : = E oplus H^{oplus (n-r-2)}, triplets (X,E,H) as above whose m_2 is small with respect to the invariants d := c_{n-2}(F) H^2 and g := 1 + (1/2)(K_X+c_1(F)+H) cdot c_{n-2}(F) cdot H are studied and classified.
ample vector bundle; special variety; surface;
Settore MAT/03 - Geometria
2010-PR0-0050 - Geometria delle Varietà Algebriche - VAN GEEMEN, LAMBERTUS - PRIN10-11 - PRIN bando 2010-11 - 2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/889369
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