Conjectures of Suciu ["Fundamental groups of line arrangements: Enumerative aspects," 43-79. Contemporary Mathematics 276. Providence, RI: American Mathematical Society, 2001.] relate the fundamental group of an arrangement complement to the first resonance variety of. We describe a connection between the first resonance variety and the Orlik-Terao algebra of the arrangement. In particular, we show that nonlocal components of give rise to determinantal syzygies of. As a result, lies on a scroll, placing geometric constraints on. The key observation is that is the homogeneous coordinate ring associated to a nef but not an ample divisor on the blowup of at the singular points of.
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