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Contractibility of space of stability conditions on the projective plane via global dimension function
Yu-Wei Fan, Chunyi Li, Wanmin Liu, Yu Qiu
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We compute the global dimension function gldim on the principal component Stab^†(ℙ²) of the space of Bridgeland stability conditions on ℙ². It admits $2$ as the minimum value and the preimage gldim⁻¹(2) is contained in the closure S̅t̅a̅b̅ᴳ̅ᵉ̅ᵒ̅(̅ℙ̅²̅)̅ of the subspace consisting of geometric stability conditions. We show that gldim⁻¹[2,x) contracts to gldim⁻¹(2) for any real number x≥2 and that gldim⁻¹(2) is contractible.
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