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Building Grothendieck topoi out of ample divisors

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We show that every single ample divisor on a complex smooth projective variety can recapture the essential information about the \linebreak sheaves on the small Zariski site of the variety. We then use it to characterize ample divisors among nef divisors topos-theoretically.

Abstract

We show that every single ample divisor on a complex smooth projective variety can recapture the essential information about the \linebreak sheaves on the small Zariski site of the variety. We then use it to characterize ample divisors among nef divisors topos-theoretically.

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