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Seshadri positive submanifolds of polarized manifolds

Lucian Bădescu, Mauro Beltrametti (2013)

Open Mathematics

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...

The trivial locus of an analytic map germ

H. Hauser, G. Muller (1989)

Annales de l'institut Fourier

We prove: For a local analytic family { X s } s S of analytic space germs there is a largest subspace T in S such that the family is trivial over T . Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

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