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Intrinsicness of the Newton polygon for smooth curves on ℙ¹ x ℙ¹

Wouter Castryck (UGent) and Filip Cools
(2017) REVISTA MATEMATICA COMPLUTENSE. 30(2). p.233-258
Author
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

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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}},
}
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