Seshadri positive submanifolds of polarized manifolds

• Autorzy: Lucian Bădescu , Mauro Beltrametti
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Seshadri constant; Seshadri A-big; Seshadri A-ample; Variety defined in a given degree; Formal rational functions; Cohomological dimension

Kategorie tematyczne

• 14F20: \'Etale and other Grothendieck topologies and (co)homologies
• 14E25: Embeddings
• 14D15: Formal methods; deformations
• 14C25: Algebraic cycles

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 3
• Strony: 447-476

Daty

wydano

2013-03-01

online

2012-12-22

Twórcy

autor

Lucian Bădescu

• Università degli Studi di Genova, Via Dodecaneso 35, 16146, Genova, Italy

autor

Mauro Beltrametti

• Università degli Studi di Genova, Via Dodecaneso 35, 16146, Genova, Italy

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Identyfikatory

DOI

10.2478/s11533-012-0146-z