A generic quartic 3-fold X admits a 7-dimensional family of representations as the Pfaffian of an 8 by 8 skew-symmetric matrix of linear forms. This provides a 7-dimensional moduli space M of rank 2 vector bundles on X. A precise geometric description of a 14-dimensional family of half-canonical curves C of genus 15 in X such that the above vector bundles are obtained by Serre's construction from C is given. It is proved that the Abel-Jacobi map of this family factors through M , and the resulting map from M …
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