On the Cox ring of blowing up the diagonal

preprint2014arXivOpen access

Abstract

We compute the Cox rings of the blow-ups BlΔ(X′×X′)\mathrm{Bl}_Δ(X'\times X') and BlΔ(P1n)\mathrm{Bl}_Δ(\mathbb P_1^n) where X′X' is a product of projective spaces and ΔΔ is the (generalised) diagonal.

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