55 citations · 170 across the 19 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…
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…