We study incompressible surfaces constructed by Culler-Shalen theory in the
context of twisted Alexander polynomials. For a 1st cohomology class of a
3-manifold the coefficients of twisted Alexander polynomials induce regular
functions on the SL2​(C)-character variety. We prove that if an
ideal point gives a Thurston norm minimizing non-separating surface dual to the
cohomology class, then the regular function of the highest degree has a finite
value at the ideal point.Comment: 10 pages, to appear in "The special issue for the 20th anniversary",
the Journal of Mathematical Sciences, the University of Toky