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arXiv · 1901.10929

Winding Number of $r$-modular sequences and Applications to the Singularity Content of a Fano Polygon

Daniel Cavey·Akihiro Higashitani
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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 basket of residual singularities is of the form $\left\{ \frac{1}{r}(1,s_{1}), \frac{1}{r}(1,s_{2}), \ldots, \frac{1}{r}(1,s_{k}) \right\}$ for $k,r \in \mathbb{Z}_{>0}$, and $1 \leq s_{i} < r$ is coprime to $r$.

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Daniel Cavey, Akihiro Higashitani. 2019-01-30. Winding Number of $r$-modular sequences and Applications to the Singularity Content of a Fano Polygon. https://arxiv.org/abs/1901.10929

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