K3 surfaces with non-symplectic automorphisms of order three and Calabi–Yau orbifolds

Let S be a K3 surface that admits a non-symplectic automorphism ρ   of order 3. We divide S×P1S×P1 by ρ×ψρ×ψ where ψ   is an automorphism of order 3 of P1P1. There exists a ramified cover of a partial crepant resolution of the quotient that is a Calabi–Yau orbifold. We compute the Euler characteristic of our examples and obtain values ranging from 30 to 219.