Global pluripotential theory over a trivially valued field

Boucksom, Sébastien; Jönsson, Mattias

doi:10.5802/afst.1705

Cited by 12 publications

(35 citation statements)

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“…When , they prove that two norms with satisfy if and only if [BJ21, Lemma 3.11 and Theorem 6.22]. The proof relies on results from non-Archimedean pluripotential developed in [BJ22].…”

Section: Relation To Global Resultsmentioning

confidence: 99%

Convexity of multiplicities of filtrations on local rings

Blum,

Liu,

2024

Compositio Math.

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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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“…When , they prove that two norms with satisfy if and only if [BJ21, Lemma 3.11 and Theorem 6.22]. The proof relies on results from non-Archimedean pluripotential developed in [BJ22].…”

Section: Relation To Global Resultsmentioning

confidence: 99%

Convexity of multiplicities of filtrations on local rings

Blum,

Liu,

2024

Compositio Math.

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“…As throughout, we assume that X is a normal projective variety defined over an algebraically closed field of characteristic zero; the boundary divisor B will be irrelevant in the present section. We refer to Reboulet [37, Section 2] or Boucksom-Jonsson [11] for further details and proofs of the results stated below.…”

Section: Berkovich Analytificationmentioning

confidence: 99%

“…Studied in [9,35], we refer to [11, Section 2.1] for further details. Definition 2.16 [11,Section 2.1]. We define a flag ideal to be a vertical fractional ideal sheaf 𝔞 on 𝑋 × A 1 (i.e., a G 𝑚 -invariant, coherent fractional ideal sheaf on 𝑋 × A 1 that is trivial on 𝑋 × G 𝑚 ).…”

Section: Berkovich Analytificationmentioning

confidence: 99%

On divisorial stability of finite covers

Dervan,

Papazachariou

2024

Forum of Mathematics, Sigma

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Divisorial stability of a polarised variety is a stronger – but conjecturally equivalent – variant of uniform K-stability introduced by Boucksom–Jonsson. Whereas uniform K-stability is defined in terms of test configurations, divisorial stability is defined in terms of convex combinations of divisorial valuations on the variety. We consider the behaviour of divisorial stability under finite group actions and prove that equivariant divisorial stability of a polarised variety is equivalent to log divisorial stability of its quotient. We use this and an interpolation technique to give a general construction of equivariantly divisorially stable polarised varieties.

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“…In this article, we will make use of envelopes of possibly non bounded metrics. We essentially reproduce the arguments of [BJ21] in the case of an arbitrary complete valued field.…”

Section: Conjecture 227 Continuity Of Envelopes Holds For Any Semiamp...mentioning

confidence: 99%