2019/01/30 by Daniel Cavey, Cavey, Daniel, Akihiro Higashitani +1
Mathematics · #14J45 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 14M25 #Secondary: 05A99. 14B05 #math.AG #math.CO #msc:05A99. #msc:14B05 #msc:14J45 #msc:14M25
paper · pdf · doi:10.48550/arxiv.1901.10929
22 pages, 4 figures
arxiv created 2019/01/30 · openalex publication_date 2019/01/30 · arxiv updated 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By generalising the notion of a unimodular sequence, we create an expression for the winding number of certain ordered sets of lattice points. Since the winding number of the vertices of a Fano polygon is necessarily one, we use this expression as a restriction to classify all Fano polygons without T-singularities and whose basket of residual singularities is of the form \ (1)/(r)(1,s1), (1)/(r)(1,s2), …, (1)/(r)(1,sk) \ for k,r ∈ ℤ>0, and 1 ≤ si < r is coprime to r.