ある種の曲面の自己同型写像と同変直線束について

In §1 it is proved that any elliptic surface without exceptional curve admits a canonical involution, which is an extension of the involution in [7]. Since a general elliptic curve admits the unique non trivial involutive isomorphism, then we will call this a canonicall one. By making use of a lemma in III [2], it is easy to construct the involution but in order to find invariant divisors, we make it concretely. Non singular surfaces of degree 4 in P^3 are K3 surfaces and one of them is a singular K3 surface. We deduce an informatiom about the homotopical cell structure of a K3 surface. Automorphisms of this surface are constructed in §2. Some of them translate a global section to another section and others do not preserve the elliptic structure. In the last section some remarks are given about clliptic modular sufaces which are singular K3 surfaces.