  The coefficients of twisted Alexander polynomials of a knot induce regular
functions of the $SL_2(\mathbb{C})$-character variety. We prove that the
function of the highest degree has a finite value at an ideal point which gives
a minimal genus Seifert surface by Culler-Shalen theory. It implies a partial
affirmative answer to a conjecture by Dunfield, Friedl and Jackson.
