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We study the twisted Alexander polynomial from the viewpoint of theSL(2,C)-character variety of nonabelian representations of a knot group. It isknown that if a knot is fibered, then the twisted Alexander polynomialsassociated with nonabelian SL(2,C)-representations are all monic. In thispaper, we show that the converse holds for 2-bridge knots. Furthermore we showthat for a 2-bridge knot there exists a curve component in theSL(2,C)-character variety such that if the knot is not fibered then there areonly finitely many characters in the component for which the associated twistedAlexander polynomials are monic. We also show that for a 2-bridge knot of genusg, in the above curve component for all but finitely many characters theassociated twisted Alexander polynomials have degree 4g-2.

TWISTED ALEXANDER POLYNOMIALS AND CHARACTER VARIETIES OF 2-BRIDGE KNOT GROUPS