Greatest lower bounds on Ricci curvature for toric Fano manifolds

By Chi Li. 2009

56 citations recorded by the source corpus.

Abstract In this short note, based on the work of Wang and Zhu (2004) [8] , we determine the greatest lower bounds on Ricci curvature for all toric Fano manifolds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4246785ecab5dbd8575bd71772f852a6261622ae

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties (2012, background): “1 gives the following theorem, which – when translated to toric geometry – generalizes the main result of [40] (see section 3.”
A variational approach to the Yau–Tian–Donaldson conjecture (2015, methodology): “d t2(0;1) there exists a Kahler form ! t2c 1(X) such that Ric(! t) = t! t+ (1 t)!: This corollary was independently established in the appendix of [CRZ18], as a consequence of [LS14, SW16] (see also [Li11] for the toric case and [Cab18] for the case of Fano -manifolds of complexity one). The nal sta”
Thresholds, valuations, and K-stability (2017, methodology): “When X is a smooth toric Fano variety, δ(−KX) agrees with the formula in [Li11] for the greatest Ricci lower bound (see [Tia92, Szé11]).”
Kähler–Einstein metrics along the smooth continuity method (2015, background): “In addition we can recover the result of Li [33] on the greatest lower bound on the Ricci curvature of toric Fano manifolds.”
On K‐stability and the volume functions of ℚ‐Fano varieties (2015, background): “visor Don Xsuch that (X,−KX) is not divisorially semistable along D. Proof. We consider the case bP 6= 0. Let cP ∈ Pbe the intersection of the boundary ∂P of Pand the half line {(1−t)bP |t∈ R≥0} (cf. [Li11]). Let FP be a facet (that is, (n− 1)-dimensional face) of P with cP ∈ FP, and let R≥0vλ be th”
K-stability of Fano varieties: an algebro-geometric approach (2020, result): “Later this invariant was further studied in [Szé11, Li11, SW16] etc.”
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, methodology): “The invariant R(X) is explicitly calculated for P2 blown up at one point by Szekelyhidi [40], and for all toric Fano manifolds by Li [21].”