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2021 Winding number of $r$-modular sequences and applications to the singularity content of a fano polygon
Daniel Cavey, Akihiro Higashitani
Tohoku Math. J. (2) 73(1): 137-158 (2021). DOI: 10.2748/tmj.20200207

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.

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Daniel Cavey. Akihiro Higashitani. "Winding number of $r$-modular sequences and applications to the singularity content of a fano polygon." Tohoku Math. J. (2) 73 (1) 137 - 158, 2021. https://doi.org/10.2748/tmj.20200207

Information

Published: 2021
First available in Project Euclid: 22 March 2021

Digital Object Identifier: 10.2748/tmj.20200207

Subjects:
Primary: 14M25
Secondary: 05A99 , 14B05 , 14J45

Keywords: $r$-modular sequence , cyclic quotient singularity , Fano polygon , singularity content , Winding number

Rights: Copyright © 2021 Tohoku University

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Vol.73 • No. 1 • 2021
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