The Hartogs extension theorem on (n – 1)-complete complex spaces

Abstract

Performing local extension from pseudoconcave boundaries along Levi-Hartogs figures and building a Morse-theoretical frame for the global control of monodromy, we establish a version of the Hartogs extension theorem which is valid in singular complex spaces (and currently not available by means of techniques), namely: For every domain Ω of an (n – 1)-complete normal complex space of pure dimension n ≧ 2, and for every compact set K ⊂ Ω such that Ω\K is connected, holomorphic or meromorphic functions in Ω\K extend holomorphically or meromorphically to Ω. Assuming that X is reduced and globally irreducible, but not necessarily normal, and that the regular part [Ω\K]reg is connected, we also show that meromorphic functions on Ω\K extend meromorphically to Ω.