Canonical syzygies of smooth curves on toric surfaces

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Castryck, Wouter^1,2,3,4  Cools, Filip¹  Demeyer, Jeroen⁴  Lemmens, Alexander¹ 

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B, B-3001 Leuven, Heverlee, Belgium

[2] Katholieke Univ Leuven, Dept Elect Engn, Kasteelpk Arenberg 10-2452, B-3000 Leuven, Heverlee, Belgium

[3] Katholieke Univ Leuven, Imec COSIC, Kasteelpk Arenberg 10-2452, B-3000 Leuven, Heverlee, Belgium

[4] Univ Ghent, Dept Math Algebra & Geometry, Krijgslaan 281-S23, B-9000 Ghent, Belgium

关键词: Algebraic curves;    Toric surfaces;    Syzygies;   

DOI  :  10.1016/j.jpaa.2019.05.018

来源: Elsevier

【 摘 要 】

In a first part of this paper, we prove constancy of the canonical graded Betti table among the smooth curves in linear systems on Gorenstein weak Fano toric surfaces. In a second part, we show that Green's canonical syzygy conjecture holds for all smooth curves of genus at most 32 or Clifford index at most 6 on arbitrary toric surfaces. Conversely we use known results on Green's conjecture (due to LelliChiesa) to obtain new facts about graded Betti tables of projectively embedded toric surfaces. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free