By Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)
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Extra info for Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983
X changes is not of Enriques One family of course the automor- always surfaces injective. 3. Thero 48 we had Y = Km(E xF), were identified s p a n n i n g for Y ~ P1 x P1 i0 curves. So face Y with an An It is of the is central or by the it seems few involution E, but Enriques with type T one of order be curves E. on The covering X leaving easily checks very of Enriques surfaces finite can EI,FI,D 1 ..... D 8 involution invariant these that T even acts similarly from a K3-sur- of a double cover Y' ÷ PlXPl locus.
Euler's Q X E - F = 2. P, follows: P xQ the is of the the divisor class in Px Q 3F+E, residual form IF[ T has In [Br i] l e n t with the Its degree with the is IFI planes computed cut out b y t h e p l a n e s bidegree (3,1) and X + P x Q P and P+TpQ(P) as through Segre also shows on X has b l o w s down some c u r v e s . Q. So = 3 d e g F + d e g E - deg P - 4 = transforms, of t h e F e r m a t q u a r t i c IEI, IE[. In f a c t it b l o w s down f o u r l i n e s m e e t i n g Using intersections TpQ(P).
Prescribed h 2I = h 22 = 0, Put z = h I + h 2 - (2r 7 + 3r 6 + 4r 5 + 5r 4 + 6r 3 + 4r 2 + 2r I + 3to). (hl-h 2) = i. take r 8 = Z-hl, r 9 = hl-h 2. 2. Geometric meanin~ One tant -2 the term on the to term In (I) be either ques effective Mori. using can proof he assumption: any nodal curves. The Ve]. curves which By ample anodality C2 = 0 only a if with B y the or c2 = 0 o and adjunction cusp). Now E, the m a i n problem Enriques divisor As usual, constructive. surface are Then With is 0x(Co)IC ° let us 0 , Ox contains < 0.
Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983 by Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)