55 citations · 170 across the 19 of their papers we have counts for
19 papers
The Elusive Relatively K-Unstable Delzant Octagon: A Numerical Search
Thibaut Delcroix, Bijan Mohammadi
Relative K-stability of toric varieties can be tested through explicit Donaldson-Futaki computations, yet finding unstable examples remains challenging. We develop a reproducible s…
On the effective YTD conjecture
Thibaut Delcroix
We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which c…
Numerical invariants for weighted cscK metrics
Thibaut Delcroix, Simon Jubert
In K-stability, the delta invariant of a Fano variety encodes the existence of Kähler-Einstein metrics. We introduce a weighted analytic delta invariant, and a reduced version, tha…
Weight sensitivity in K-stability of Fano varieties
Thibaut Delcroix
We prove that, for a spherical Fano threefold not in the Mori-Mukai family 2-29, and a weight function associated with the action of the connected center of a Levi subgroup of its…
CscK metrics on rank one spherical Fano fourfolds
Thibaut Delcroix
This four-pages note is an invitation to explore explicit K-stability for arbitrary Kähler classes of low dimension and low rank spherical varieties. We apply our simple combinator…
SYZ and optimal transport stability of Weyl polytopes
Thibaut Delcroix, Jakob Hultgren
We prove optimal transport stability (in the sense of Andreasson and the second author) for reflexive Weyl polytopes: reflexive polytopes which are convex hulls of an orbit of a We…
Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces
Thibaut Delcroix
We consider families of conical Kähler-Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, whi…
Spherical actions on locally factorial Fano varieties of dimension and rank
Thibaut Delcroix, Pierre-Louis Montagard
We obtain the exhaustive list of 337 faithful spherical actions of rank two or less on locally factorial Fano manifolds of dimension four or less. As a preliminary step, we determi…
An effective weighted K-stability condition for polytopes and semisimple principal toric fibratons
Thibaut Delcroix, Simon Jubert
The second author has shown that existence of extremal Kähler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off f…
The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
Thibaut Delcroix
We prove the Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a compact Lie group with at leas…
Uniform K-stability of polarized spherical varieties
Thibaut Delcroix
We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial…
Examples of K-unstable Fano manifolds
Thibaut Delcroix
We examine various examples of horosymmetric manifolds which exhibit interesting properties with respect to canonical metrics. In particular, we determine when the blow-up of a qua…
Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
Thibaut Delcroix, Jakob Hultgren
We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get…
Ricci flat Kähler metrics on rank two complex symmetric spaces
Olivier Biquard, Thibaut Delcroix
We obtain Ricci flat Kähler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compact…
K{ä}hler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional
Thibaut Delcroix
We introduce a class of almost homogeneous varieties contained in the class of spherical varieties and containing horospherical varieties as well as complete symmetric varieties. W…
K-Stability of Fano spherical varieties
Thibaut Delcroix
We prove a criterion for K-stability of a -Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some comb…
Log canonical thresholds on group compactifications
Thibaut Delcroix
We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex re…
Kähler-Einstein metrics on group compactifications
Thibaut Delcroix
We obtain a necessary and sufficient condition of existence of a K{ä}hler-Einstein metric on a -equivariant Fano compactification of a complex connected reductive group…
Alpha-invariant of Toric Line Bundles
Thibaut Delcroix
We generalize the work of Jian Song to compute the alpha invariant of any (nef and big) toric line bundle in terms of the associated polytope. We use the analytic version of the co…