
Intrinsicness of the Newton polygon for smooth curves on ℙ¹ x ℙ¹
- Author
- Wouter Castryck (UGent) and Filip Cools
- Organization
- Abstract
- Let C be a smooth projective curve in of genus , and assume that it is birationally equivalent to a curve defined by a Laurent polynomial that is non-degenerate with respect to its Newton polygon . Then we show that the convex hull of the interior lattice points of is a standard rectangle, up to a unimodular transformation. Our main auxiliary result, which we believe to be interesting in its own right, is that the first scrollar Betti numbers of -non-degenerate curves are encoded in the combinatorics of , if satisfies some mild conditions.
- Keywords
- Non-degenerate curve, Toric surface, Lattice polygon, Scrollar invariants, CANONICAL CURVES
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8568135
- MLA
- Castryck, Wouter, and Filip Cools. “Intrinsicness of the Newton Polygon for Smooth Curves on ℙ1 x ℙ1.” REVISTA MATEMATICA COMPLUTENSE, vol. 30, no. 2, 2017, pp. 233–58, doi:10.1007/s13163-017-0224-7.
- APA
- Castryck, W., & Cools, F. (2017). Intrinsicness of the Newton polygon for smooth curves on ℙ1 x ℙ1. REVISTA MATEMATICA COMPLUTENSE, 30(2), 233–258. https://doi.org/10.1007/s13163-017-0224-7
- Chicago author-date
- Castryck, Wouter, and Filip Cools. 2017. “Intrinsicness of the Newton Polygon for Smooth Curves on ℙ1 x ℙ1.” REVISTA MATEMATICA COMPLUTENSE 30 (2): 233–58. https://doi.org/10.1007/s13163-017-0224-7.
- Chicago author-date (all authors)
- Castryck, Wouter, and Filip Cools. 2017. “Intrinsicness of the Newton Polygon for Smooth Curves on ℙ1 x ℙ1.” REVISTA MATEMATICA COMPLUTENSE 30 (2): 233–258. doi:10.1007/s13163-017-0224-7.
- Vancouver
- 1.Castryck W, Cools F. Intrinsicness of the Newton polygon for smooth curves on ℙ1 x ℙ1. REVISTA MATEMATICA COMPLUTENSE. 2017;30(2):233–58.
- IEEE
- [1]W. Castryck and F. Cools, “Intrinsicness of the Newton polygon for smooth curves on ℙ1 x ℙ1,” REVISTA MATEMATICA COMPLUTENSE, vol. 30, no. 2, pp. 233–258, 2017.
@article{8568135, abstract = {{Let C be a smooth projective curve in of genus , and assume that it is birationally equivalent to a curve defined by a Laurent polynomial that is non-degenerate with respect to its Newton polygon . Then we show that the convex hull of the interior lattice points of is a standard rectangle, up to a unimodular transformation. Our main auxiliary result, which we believe to be interesting in its own right, is that the first scrollar Betti numbers of -non-degenerate curves are encoded in the combinatorics of , if satisfies some mild conditions.}}, author = {{Castryck, Wouter and Cools, Filip}}, issn = {{1139-1138}}, journal = {{REVISTA MATEMATICA COMPLUTENSE}}, keywords = {{Non-degenerate curve,Toric surface,Lattice polygon,Scrollar invariants,CANONICAL CURVES}}, language = {{eng}}, number = {{2}}, pages = {{233--258}}, title = {{Intrinsicness of the Newton polygon for smooth curves on ℙ¹ x ℙ¹}}, url = {{http://dx.doi.org/10.1007/s13163-017-0224-7}}, volume = {{30}}, year = {{2017}}, }
- Altmetric
- View in Altmetric
- Web of Science
- Times cited: