Connectedness of the Fibers of a Liouvillian Function

  • Emmanuel Paul

    Université Paul Sabatier, Toulouse, France

Abstract

Let be a normal crossing divisor in a complex analytic manifold of dimension , and let be a closed logarithmic one-form, with poles on . Under appropriate hypothesis, we prove the connectedness of the fibers for a primitive of in “good” neighborhoods of . We deduce the connectedness of the fibers of Liouvillian functions of type at the origin of , under two conditions: the first extends the usual notion that “ 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

DOI 10.2977/PRIMS/1195145325