Juan G. Escudero

Universidad de Oviedo

Several techniques from algebra, geometry, topology and astronomy have been some of the guides of the formalization procedures in the temporal and spatial domains. However, it is not so much the process as the final result that characterises the works based on such methods.

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Folding polynomials of degree d with integer coefficients were used by S. Chmutov to generate complex algebraic surfaces with many ordinary double points ("Examples of projective surfaces with many singularities". J. Algebraic Geom. Vol.1, p.191 (1992)). For d=3n, there is a family of complex surfaces having more singularities, which can be obtained by using certain bivariate polynomials Q with complex coefficients. As the folding polynomials, Q are related to the generalized cosine associated with the affine Weyl group of the root system A2. ("On a family of complex algebraic surfaces of degree 3n". C. R. Math. Acad. Sci. Paris. Vol.351, n.17-18, p.699 (2013)).

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