Annali di Matematica Pura ed Applicata (1923 -)

, Volume 197, Issue 5, pp 1613–1629 | Cite as

Singular and Calabi–Yau varieties linked with billiard trajectories and diffusion operators

  • Juan García Escudero


The images under a certain map of periodic billiard trajectories inside the fundamental region of the affine Weyl group of the root system \(A_{2}\) are closed curves and configurations of lines described by a one-parameter family of polynomials. The polynomials are related with eigenvectors of symmetric diffusion operators connected with the deltoid. Several associated singular varieties and Calabi–Yau threefolds defined over the rationals are constructed.


Algebraic hypersurfaces Singularities Calabi–Yau threefolds 

Mathematics Subject Classification

Primary 14J70 Secondary 14J17 14J32 35K05 


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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de OviedoOviedoSpain

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