Affiliation:
1. Faculty of Mathematics and Computer Science University of Bucharest Bucharest Romania
2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy Bucharest Romania
Abstract
AbstractIn this article, we prove that the blow‐up of an lcK space along a subspace that verifies certain conditions is lcK if and only if is induced gcK, generalizing a theorem of Ornea–Verbitsky–Vuletescu to singular locally irreducible spaces. We also show that even if modifications of lcK spaces are not always of lcK type, they always admit quasi‐lcK metrics.
Reference16 articles.
1. Convexité topologique et prolongement des fonctions continues;Cauty R.;Compositio Math.,1973
2. M.Colţoiu A positivity theorem for modifications of projective algebraic spaces IMAR Preprint Series in Mathematics No.2/1986 http://imar.ro/~increst/1986/2_1986.pdf.
3. J.‐P.Demailly Complex analytic and differential geometry https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf
4. On the blowing down of analytic spaces
5. �ber Modifikationen und exzeptionelle analytische Mengen