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Creators/Authors contains: "Blum, Harold"

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  1. ; ; (, Compositio Mathematica)
    We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a consequence, we prove that the volume of a valuation is log convex on simplices of quasi-monomial valuations and give a new proof of a theorem of Xu and Zhuang on the uniqueness of normalized volume minimizers. In another direction, we generalize a theorem of Rees on multiplicities of ideals to filtrations and characterize when the Minkowski inequality for filtrations is an equality under mild assumptions. 
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  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. ; (, Annales scientifiques de l'École Normale Supérieure)
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  4. ; ; (, Duke Mathematical Journal)
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  5. ; ; ; (, Selecta Mathematica)
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  6. ; ; ; (, Inventiones mathematicae)
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  7. ; (, Advances in Mathematics)
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  8. ; ; ; (, Inventiones mathematicae)
    null (Ed.)
    We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space. 
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  9. ; (, Annals of Mathematics)
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