Vanishing sequences and Okounkov bodies
By S. Boucksom, Alex Kuronya, C. Maclean, Tomasz Szemberg. 2013
48 citations recorded by the source corpus.
We define and study the vanishing sequence along a real valuation of sections of a line bundle on a normal projective variety. Building on previous work of the first author with Huayi Chen, we prove an equidistribution result for vanishing sequences of large powers of a big line bundle, and study the limit measure; in particular, the latter is described in terms of restricted volumes for divisorial valuations. We also show on an example that the associated concave function on the Okounkov body can be discontinuous at boundary points.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/19510852cd4698fdebb7a996ad0e490614e76ed0
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Kähler–Einstein metrics and volume minimization (2016, background): “[Li15a, Proposition 1.2] there exists a constant c= c(X,o) such that v≤ cAX(v)ordo. So it’s easy to see that e(S•,F) ≤ cAX(v) · emax(S•,Ford o ) <+∞. The second inequality follows from the work in [BKMS14]. It is clear that FxSm = Sm for x≤ 0. Hence we may choose e− = 0. The graded family of idea”
- A variational approach to the Yau–Tian–Donaldson conjecture (2015, background): “By [BC11, BKMS15], the vanishing sequence of v on mL , scaled by 1 /m , equidistributes as m → ∞ .”
- K-stability of Fano varieties via admissible flags (2020, unknown): “We also define the pseudo-effective threshold as We say that v is of linear growth if 𝑇 ( 𝐿 ; 𝑣 ) < ∞ (e.g., when v is divisorial or has finite discrepancy; see [11, Section 2.3] and [2, Section 3.1]).”
- Thresholds, valuations, and K-stability (2017, methodology): “m estimates 1 n+1 T(v) S(v) T(v) that are proved along the way. When Lis ample and vis divisorial, the stronger inequality S(v) n n+1 T(v) was proved by Fujita [Fuj19c]. We deduce from results in [BKMS16] that the invariants S(v) and T(v) only depend on the numerical equivalence class of L. By Theo”