Let $E_i\!: y_i^2 = f(x_i)$ be two copies of a supersingular elliptic curve over a field of odd characteristics. Consider the involution $$ i\!: E_1\times E_2 \to E_1\times E_2,\qquad (x_1, y_1, x_2, y_2) \mapsto (x_2, -y_2, x_1, -y_1) $$ and the quotient $S := E_1\times E_2/i$. Is it a K3 surface? What is (are) its defining equation(s)?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.