Let $\ce$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors $K_X + (t-r) \det \ce$ when $t \ge \dim X$ and $t>r$. As an application, we classify pairs $(X,\ce)$ with $c_r$-sectional genus zero.

Keywords:

ample vector bundle, adjunction, sectional genus ample vector bundle, adjunction, sectional genus

MSC Classifications:

14J60, 14C20, 14F05, 14J40 show english descriptions Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Divisors, linear systems, invertible sheaves
Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
$n$-folds ($n>4$) 14J60 - Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
14C20 - Divisors, linear systems, invertible sheaves
14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
14J40 - $n$-folds ($n>4$)

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