On the Degeneracy Conditions for Tri-modular Simple K3 Singularities

Defining equations of tri-modular simple K3 singularities are 7 types. The defining equations of simple K3 singularities are polynomials with parameter coefficients. We can obtain degeneracy conditions of these singularities by using computer algebra system. The forms of Groebner bases generated by polynomials depend on the values of parameters, and those calculations are not easy. In this paper, we try to decide the degeneracy conditions of tri-modular simple K3 singularities. And we show examples of the calculations.