Seshadri positive submanifolds of polarized manifolds

Lucian Bădescu; Mauro Beltrametti

Open Mathematics (2013)

  • Volume: 11, Issue: 3, page 447-476
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Lucian Bădescu, and Mauro Beltrametti. "Seshadri positive submanifolds of polarized manifolds." Open Mathematics 11.3 (2013): 447-476. <http://eudml.org/doc/269775>.

@article{LucianBădescu2013,
abstract = {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.},
author = {Lucian Bădescu, Mauro Beltrametti},
journal = {Open Mathematics},
keywords = {Seshadri constant; Seshadri A-big; Seshadri A-ample; Variety defined in a given degree; Formal rational functions; Cohomological dimension; formal rational functions},
language = {eng},
number = {3},
pages = {447-476},
title = {Seshadri positive submanifolds of polarized manifolds},
url = {http://eudml.org/doc/269775},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Lucian Bădescu
AU - Mauro Beltrametti
TI - Seshadri positive submanifolds of polarized manifolds
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 447
EP - 476
AB - 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.
LA - eng
KW - Seshadri constant; Seshadri A-big; Seshadri A-ample; Variety defined in a given degree; Formal rational functions; Cohomological dimension; formal rational functions
UR - http://eudml.org/doc/269775
ER -

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