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.)

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

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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 ....

3. ,pn to def. a generic (in fact i, Auxiliary results let D invertible this be a sheaf hypothesis reduced of 2-torsion, is not be the points of intersection of We h a v e therefore the exact plane needed) D with curve of degree and let R be to D: let then n, a line R. sequence n (11) 0 Remark a ) for , L([(n-3)/2]) , L([(n-3)/2]+l) 12. The exact cohomology n sequence , @ i=i ¢ * 0 Pi associated to (Ii) gives: o d d a n isomorphism n r: H°(L(n-l)/2) C i=l b) for n Pi even an exact sequence n 0 where duality.

Of P l e a v i n g { Pl . . . p4} i n v a r i a n t 12 if E=E~0. ~6-symmetry. The equals 4 if E/Ei,E ~ So we h a v e t h e f o l l o w i n g t a b l e . n u m b e r of lines on S E ~F 16 E = F ~ Ei,E00 32 E= 48 F= E l E = F = Eco Here, in passing, the 64 following theorem of Segre [ Se 2] should be mentioned : T h e r e i s no s m o o t h q u a r t i c It would be desirable to with more than have a 64 l i n e s on i t . l a t t i c e - t h e o r e t i c proof of t h i s fact. Notice also t h a t the maximal number of l i n e s on a smooth q u i n t i c i s unknown.

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