A combinatorial interpretation for Schreyer's tetragonal invariants

Journal Article

2015

Permanent link to this Item
http://hdl.handle.net/11427/34408
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CastryckWouter_A_combinatorial_2015.pdf (208.61 KB)
Authors
Castryck, Wouter
Cools, Filip
Journal Title

Documenta Mathematica

Link to Journal
https://dx.doi.org/10.7196/sajs.718
Journal ISSN
Volume Title
Publisher
Publisher
Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
License
Series
Abstract
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.
Description
Keywords
Mathematics and Statistics
CURVES

Reference:

Castryck, W. & Cools, F. 2015. A combinatorial interpretation for Schreyer's tetragonal invariants. Documenta Mathematica. 20(4):903 - 918. http://hdl.handle.net/11427/34408

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