A combinatorial interpretation for Schreyer's tetragonal invariants

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dc.contributor.authorCastryck, Wouter
dc.contributor.authorCools, Filip
dc.date.accessioned2021-10-08T06:55:04Z
dc.date.available2021-10-08T06:55:04Z
dc.date.issued2015
dc.description.abstractSchreyer 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.
dc.identifier.apacitationCastryck, W., & Cools, F. (2015). A combinatorial interpretation for Schreyer's tetragonal invariants. <i>Documenta Mathematica</i>, 20(4), 903 - 918. http://hdl.handle.net/11427/34408en_ZA
dc.identifier.chicagocitationCastryck, Wouter, and Filip Cools "A combinatorial interpretation for Schreyer's tetragonal invariants." <i>Documenta Mathematica</i> 20, 4. (2015): 903 - 918. http://hdl.handle.net/11427/34408en_ZA
dc.identifier.citationCastryck, W. & Cools, F. 2015. A combinatorial interpretation for Schreyer's tetragonal invariants. <i>Documenta Mathematica.</i> 20(4):903 - 918. http://hdl.handle.net/11427/34408en_ZA
dc.identifier.issn1431-0635
dc.identifier.issn1431-0643
dc.identifier.ris TY - Journal Article AU - Castryck, Wouter AU - Cools, Filip AB - 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. DA - 2015 DB - OpenUCT DP - University of Cape Town IS - 4 J1 - Documenta Mathematica LK - https://open.uct.ac.za PY - 2015 SM - 1431-0635 SM - 1431-0643 T1 - A combinatorial interpretation for Schreyer's tetragonal invariants TI - A combinatorial interpretation for Schreyer's tetragonal invariants UR - http://hdl.handle.net/11427/34408 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/34408
dc.identifier.vancouvercitationCastryck W, Cools F. A combinatorial interpretation for Schreyer's tetragonal invariants. Documenta Mathematica. 2015;20(4):903 - 918. http://hdl.handle.net/11427/34408.en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.sourceDocumenta Mathematica
dc.source.journalissue4
dc.source.journalvolume20
dc.source.pagination903 - 918
dc.source.urihttps://dx.doi.org/10.7196/sajs.718
dc.subject.otherMathematics and Statistics
dc.subject.otherCURVES
dc.titleA combinatorial interpretation for Schreyer's tetragonal invariants
dc.typeJournal Article
uct.type.publicationResearch
uct.type.resourceJournal Article
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