Geodesic
A combinatorial interpretation for Schreyer's tetragonal invariants
Documenta mathematica, Tome 20 (2015), pp. 927-942
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Schreyer has proved that the graded Betti numbers of a canonical tetragonal curve are determined by two integers b1​ and b2​, 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.
DOI : 10.4171/dm/509
Classification : 14H45, 14M25 
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     author = {Wouter Castryck and Filip Cools},
     title = {A combinatorial interpretation for {Schreyer's} tetragonal invariants},
     journal = {Documenta mathematica},
     pages = {927--942},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/509},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/509/}
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Wouter Castryck; Filip Cools. A combinatorial interpretation for Schreyer's tetragonal invariants. Documenta mathematica, Tome 20 (2015), pp. 927-942. doi: 10.4171/dm/509

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