Generalized polarized manifolds with low second class

2016/08/27 by Lanteri, Antonio, Tironi, Andrea Luigi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.07732

Abstract

On a smooth complex projective variety X of dimension n, consider an ample vector bundle E of rank r ≤ n-2 and an ample line bundle H. A numerical character m₂=m₂(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 ⊕ H^{⊕ (n-r-2)}, triplets (X,E,H) as above whose m₂ is small with respect to the invariants d:=c_n-2(F)H² and g:=1+(1)/(2)(K_X + c₁(F)+H) ⋅ c_n-2(F) ⋅ H are studied and classified.

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