The K3 surfaces are characterized by the following properties: their canonical class is equal to zero; they do not possess (in contrast to abelian varieties) regular one-dimensional differential forms. The author studies special symmetric reflections of the varieties of the type \((E \times S)/(j,i)\), where \(S\) is a K3 surface equipped with involution \(i\), and \(E\) is an elliptic curve with involution \(j\) such that \(E/j \simeq \mathbb{P}^ 1\). In this connection the corresponding results of V. V. Nikulin are used.
For the entire collection see [Zbl 0790.00001].