Download Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a by Enrico Arbarello, Corrado De Concini (auth.), Eduard PDF

By Enrico Arbarello, Corrado De Concini (auth.), Eduard Casas-Alvero, Gerald Welters, Sebastian Xambó-Descamps (eds.)

ISBN-10: 3540152326

ISBN-13: 9783540152323

ISBN-10: 3540396438

ISBN-13: 9783540396437

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Additional resources for Algebraic Geometry Sitges (Barcelona) 1983: Proceedings of a Conference held in Sitges (Barcelona), Spain October 5–12, 1983

Example text

D 8 -2, Of induces smooth = y/c~ two I the however. 2) of type curves On i preserves 2EI,2E 2 pencil more. c a n be used as b r a n c h in surface each act on the configuration Since that fixed points. from the two once Y' introduced o The such R = y piXQ u U3 Pxqj is a involution IFx[ be Then cover blown consider sublattice in H2(X,~). which 41 3. 1. The Enriques An surfaces lattice Enriques surface X = Y/(y has Euler n u m b e r e(X) = _I e ( Y ) = 12 2 and bl(X) = 0. This implies = Hl(X'TZ)tors = ITI(X) = 2£2' b2(X) = i0.

E. such Any class by ~E theorem (Nakai-Moisezon again two acts trivially on E l C L. Z )/torsion, also holds: for k~ihler effective is F strong on g E O+(E) that for generic yE c = p'a, of a n general" the $/ = g * to find take of some Aut(X) it is not clear that But the converse Take ~{ @ Y IE I = id of of Each So all Of course necessarily action ÷ O+(E). is "sufficiently Horikawa's to the Aut(X) to the double to study too. class the in class Altogether 47 For a generic Enriques surface r the 2-congruence subgroup The on We knowledge X.

The 16 2-torsion points X' = A/t in replacing X = Km(A), torus, some discrete s u b g r o u p a--+-a. 16 images them, surface A with involution points. of a complex the double Pl ..... trivial t IF. P4 E p, extensions containing t = S8 exhibiting PlXQ X' as double u ... u p g x Q u p x q l u cover of the P×Q quadric with branch curve ... u pxq4. ql q2 q3 l q4 Pl The B, of the smooth blow-up X~, B Pi x Q (over and the surfaces of Px Q consists of the P × qi" blown up P2 X = Km(E× in the (smooth These points) we guration of nodal curves on P3 X.

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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.)


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