Collections exceptionnelles sur certains espaces de Hassett
Résumé
We construct an S2 × Sn invariant full exceptional collection on Hassett spaces of weighted stable rational curves with n + 2 markings and weights (12 + η, 12 + η, n1 ,. . ., n1 ), for 0 < η 1. These Hassett spaces can be identified with the symmetric GIT quotients of (P1)n by the diagonal action of Gm, when n is odd, and their Kirwan desingularization, when n is even. The existence of such an exceptional collection is one of the needed ingredients in order to prove the existence of a full Sn-invariant exceptional collection on M0,n. To prove exceptionality we use the method of windows in derived categories. To prove fullness we use previous work on the existence of invariant full exceptional collections on Losev–Manin spaces.
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