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 ℙ^{1} x ℙ^{1}.” REVISTA MATEMATICA COMPLUTENSE 30.2 (2017): 233–258. Print.
- APA
- Castryck, W., & Cools, F. (2017). Intrinsicness of the Newton polygon for smooth curves on ℙ^{1} x ℙ^{1}. REVISTA MATEMATICA COMPLUTENSE, 30(2), 233–258.
- Chicago author-date
- Castryck, Wouter, and Filip Cools. 2017. “Intrinsicness of the Newton Polygon for Smooth Curves on ℙ^{1} x ℙ^{1}.” Revista Matematica Complutense 30 (2): 233–258.
- Chicago author-date (all authors)
- Castryck, Wouter, and Filip Cools. 2017. “Intrinsicness of the Newton Polygon for Smooth Curves on ℙ^{1} x ℙ^{1}.” Revista Matematica Complutense 30 (2): 233–258.
- Vancouver
- 1.Castryck W, Cools F. Intrinsicness of the Newton polygon for smooth curves on ℙ^{1} x ℙ^{1}. REVISTA MATEMATICA COMPLUTENSE. 2017;30(2):233–58.
- IEEE
- [1]W. Castryck and F. Cools, “Intrinsicness of the Newton polygon for smooth curves on ℙ^{1} x ℙ^{1},” 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}, }
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