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Creators/Authors contains: "Zhuang, Ziquan"

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  1. ( , Journal of Algebraic Geometry)
    Recent study in K-stability suggests that Kawamata log terminal (klt) singularities whose local volumes are bounded away from zero should be bounded up to special degeneration. We show that this is true in dimension three, or when the minimal log discrepancies of Kollár components are bounded from above. We conjecture that the minimal log discrepancies of Kollár components are always bounded from above, and verify it in dimension three when the local volumes are bounded away from zero. We also answer a question from Han, Liu, and Qi on the relation between log canonical thresholds and local volumes. 
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    Free, publicly-accessible full text available January 25, 2025
  2. ; ; ; ( , Forum of Mathematics, Pi)
    Abstract We prove an algebraic version of the Hamilton–Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler–Ricci soliton when the ground field . 
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  3. ; ; ( , Annals of Mathematics)
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  4. ; ( , Forum of Mathematics, Pi)
    Abstract We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications. 
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  5. ; ( , Cambridge Journal of Mathematics)
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  6. ; ( , Annals of mathematics)
    null (Ed.)
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  7. ; ( , Annals of mathematics)
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