Tohoku Mathematical Journal
2021
March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 137-158

Title WINDING NUMBER OF $r$-MODULAR SEQUENCES AND APPLICATIONS TO SINGULARITY CONTENT OF A FANO POLYGON

Author Daniel Cavey and Akihiro Higashitani

(Received April 8, 2019, revised December 4, 2019)
Abstract. 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 singularities in the basket of residual singularities all have equal Gorenstein index.

Mathematics Subject Classification. Primary 14M25; Secondary 05A99, 14B05, 14J45.
Key words and phrases. Fano polygon, cyclic quotient singularity, singularity content, $r$-modular sequence, winding number.

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