Q 5 étant l'orbite des vecteurs de plus haut poids de ? 2,0 , elle est intersection de quadriques. En notant I Q 5 /P(S 2 V ) l'idéal des équations de Q 5 dans P(S 2 V ) = P(? 2,0 ? C), I Q 5 /P(S 2 V ) (2) est alors engendré par ses sections, La suite exacte 0 ? I Z 5 /P(S 2 V ) (2) ? I Z/P(S 2 V ) (2) ? I Z ,
Nous avons la suite exacte courte : 0 ? I Z 5 (3) ? O Z (3) ? O Z ,
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