Summary
Let ϱ: X→Y be an étale double covering, where Y is a K3 surface and X a smooth Enriques' surface; by interchanging the sheets of ϱY carries an involution i of order two. The main result of this note is the equivalence of the following conditions: 1) Y is the base locus of a net of (special) quadrics of P5 and the involution i extends to a projective one inP 5; 2) X contains a net of irreducible non hyperelliptic curves of arithmetic genusp a=3; 3) X contains two divisors D1, D2 such that pa(Di)=h0(Di)=1, i=1, 2, (D1, D2)=2 and ¦D1+D2¦has no fixed, components.
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Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R.
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Verra, A. Superfici di Enriques e reti di quadriche. Annali di Matematica pura ed applicata 130, 307–320 (1982). https://doi.org/10.1007/BF01761500
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DOI: https://doi.org/10.1007/BF01761500