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arXiv · 1609.02360

Canonical syzygies of smooth curves on toric surfaces

Wouter Castryck·Filip Cools·Jeroen Demeyer·Alexander Lemmens
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Abstract

In a first part of this paper, we prove constancy of the canonical graded Betti table among the smooth curves in linear systems on Gorenstein weak Fano toric surfaces. In a second part, we show that Green's canonical syzygy conjecture holds for all smooth curves of genus at most 32 or Clifford index at most 6 on arbitrary toric surfaces. Conversely we use known results on Green's conjecture (due to Lelli-Chiesa) to obtain new facts about graded Betti tables of projectively embedded toric surfaces.

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Wouter Castryck, Filip Cools, Jeroen Demeyer, Alexander Lemmens. 2016-09-08. Canonical syzygies of smooth curves on toric surfaces. https://arxiv.org/abs/1609.02360

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