Let D be a normal crossing divisor in a complex analytic manifold of dimension n, and let Ω be a closed logarithmic one-form, with poles on D. Under appropriate hypothesis, we prove the connectedness of the fibers for a primitive of Ω in "good" neighborhoods of D. We deduce the connectedness of the fibers of Liouvillian functions of type f= _f_1λ 1 ⋯ fp_λ_p at the origin of Cn, under two conditions: the first extends the usual notion that "f is not a power". The second excludes certain meromorphic functions.
Cite this article
Emmanuel Paul, Connectedness of the Fibers of a Liouvillian Function. Publ. Res. Inst. Math. Sci. 33 (1997), no. 3, pp. 465–481