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In this paper we show that semistable vector bundles on a Castelnuovo curveof genus g >= 2 have theta divisors. As a corollary, we deduce that semistablevector bundles on a smooth, general curve of genus g >= 2 which extend tosemistable vector bundles on any Castelnuovo degeneration of the general curveadmit a theta divisor.

Vector bundles with Theta divisors I: Bundles on Castelnuovo curves