Let be an ample vector bundle on a projective manifold , with a section vanishing on a smooth subvariety of the expected dimension, and let be an ample line bundle on inducing a very ample ample line bundle on . Triplets as above are classified assuming that , embedded by , is a variety of small degree with respect to codimension.
Antonio LANTERI. Carla NOVELLI. "Varieties of small degree with respect to codimension and ample vector bundles." J. Math. Soc. Japan 60 (2) 341 - 361, April, 2008. https://doi.org/10.2969/jmsj/06020341