We investigate the pairs $(X,\cE)$ consisting of a smooth complex projective variety $X$ of dimension $n$ and an ample vector bundle $\cE$ of rank $n-1$ on $X$ such that $\cE$ has a section whose zero locus is a smooth elliptic curve.

MSC Classifications:

14J60, 14F05, 14J40 show english descriptions Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
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]
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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