Let Y be a submanifold of dimension y of a polarized complex manifold (X, A) of dimension k ≥ 2, with 1 ≤ y ≤ k−1. We define and study two positivity conditions on Y in (X, A), called Seshadri A-bigness and (a stronger one) Seshadri A-ampleness. In this way we get a natural generalization of the theory initiated by Paoletti in [Paoletti R., Seshadri positive curves in a smooth projective 3-fold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 1996, 6(4), 259–274] (which corresponds to the case (k, y) = (3, 1)) and subsequently generalized and completed in [Bădescu L., Beltrametti M.C., Francia P., Positive curves in polarized manifolds, Manuscripta Math, 1997, 92(3), 369–388] (regarding curves in a polarized manifold of arbitrary dimension). The theory presented here, which is new even if y = k − 1, is motivated by a reasonably large area of examples.
@article{bwmeta1.element.doi-10_2478_s11533-012-0146-z,
author = {Lucian B\u adescu and Mauro Beltrametti},
title = {Seshadri positive submanifolds of polarized manifolds},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {447-476},
zbl = {1276.14022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0146-z}
}
Lucian Bădescu; Mauro Beltrametti. Seshadri positive submanifolds of polarized manifolds. Open Mathematics, Tome 11 (2013) pp. 447-476. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0146-z/
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