A Combinatorial Interpretation for Schreyer's Tetragonal Invariants

\noindent Schreyer has proved that the graded Betti numbers of a canonical tetragonal curve are determined by two integers $b_1$ and $b_2$, associated to the curve through a certain geometric construction. In this article we prove that in the case of a smooth projective tetragonal curve on a toric surface, these integers have easy interpretations in terms of the Newton polygon of its defining Laurent polynomial. We can use this to prove an intrinsicness result on Newton polygons of small lattice width.noindent \emph{MSC2010:} Primary 14H45, Secondary 14M25

2010 Mathematics Subject Classification:

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