A combinatorial interpretation for Schreyer's tetragonal invariants
- Author
- Wouter Castryck (UGent) and Filip Cools
- Organization
- 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.
- Keywords
- CURVES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7025898
- MLA
- Castryck, Wouter, and Filip Cools. “A Combinatorial Interpretation for Schreyer’s Tetragonal Invariants.” DOCUMENTA MATHEMATICA, vol. 20, 2015, pp. 903–18.
- APA
- Castryck, W., & Cools, F. (2015). A combinatorial interpretation for Schreyer’s tetragonal invariants. DOCUMENTA MATHEMATICA, 20, 903–918.
- Chicago author-date
- Castryck, Wouter, and Filip Cools. 2015. “A Combinatorial Interpretation for Schreyer’s Tetragonal Invariants.” DOCUMENTA MATHEMATICA 20: 903–18.
- Chicago author-date (all authors)
- Castryck, Wouter, and Filip Cools. 2015. “A Combinatorial Interpretation for Schreyer’s Tetragonal Invariants.” DOCUMENTA MATHEMATICA 20: 903–918.
- Vancouver
- 1.Castryck W, Cools F. A combinatorial interpretation for Schreyer’s tetragonal invariants. DOCUMENTA MATHEMATICA. 2015;20:903–18.
- IEEE
- [1]W. Castryck and F. Cools, “A combinatorial interpretation for Schreyer’s tetragonal invariants,” DOCUMENTA MATHEMATICA, vol. 20, pp. 903–918, 2015.
@article{7025898,
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.}},
author = {{Castryck, Wouter and Cools, Filip}},
issn = {{1431-0643}},
journal = {{DOCUMENTA MATHEMATICA}},
keywords = {{CURVES}},
language = {{eng}},
pages = {{903--918}},
title = {{A combinatorial interpretation for Schreyer's tetragonal invariants}},
volume = {{20}},
year = {{2015}},
}