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London to equal sums of sixth powers M. Soc. , Rapoport, M. On the Torelli theorem for kHhlerian K3-surfaces. Ann. Sci. , 8, 235-274 (1975) C 1 Cossec, F. Projective models of Enriques surfaces To appear C 2 in Math. Ann. Cossec, F. Reye congruences To appear in Trans. AMS n the symmetric 56 C3 Cossec, F. On Enriques surfaces Preprint D Dieudonn~, J. La g~om4trie des g r o u p e s c l a s s i q u e s Erg. d. Math. F. 5, S p r i n g e r (1955) Do Dolgachev, I. On automorphisms of E n r i q u e s s u r f a c e s H H i r z e b r u c h , F.

E. there exist are linearly independent vectors. D. Lemma Let 10. Assume that V there and are to K independent linear forms from V to K d I ..... d k independent linear forms from W to K b I ..... = ± 1 1 given , K 2k , is an isomorphism. Take on V the basis eib i) { d I .... ,dk}. to the linear m a p and associate in Let further E (k × k) same V one dual to the of linear forms from Then Proof. -,a k • be matrix. dimension =k . -,c k (a i W of Let V analogous be the dual A to by W , to for i=l ....

The i n t e r T h e two i s o - The form hence Denote an cox deter- orientation But K3-surfaces between X [S-l]. isomorphism of positive L coX , on latti- hence the isomorphism class is determined already by the TX : theorem for singular isomorphism Proof. positive Picard determines the opposed orientation. So the e m b e d d e d abstract oriented lattice 1:1 maximal with its orientation determines by Torelli with 2-dimensional l~-isomorphism ce (i) for all contains deflnfte three The m a p classes of s i n g u l a r even oriented factors X + Tx It.