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arXiv · 1811.01105

Projecting Syzygies of Curves

Michael Kemeny
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Abstract

We explore the concept of projections of syzygies and prove two new technical results; we firstly give a precise characterization of syzygy schemes in terms of their projections, secondly, we prove a converse to Aprodu's Projection Theorem. Applying these results, we prove that extremal syzygies of general curves of non-maximal gonality embedded by a linear system of sufficiently high degree arise from scrolls. Lastly, we prove Green's Conjecture for general covers of elliptic curves (of arbitrary degree) as well as proving a new result for curves of even genus and maximal gonality.

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Michael Kemeny. 2019-10-25. Projecting Syzygies of Curves. https://arxiv.org/abs/1811.01105

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