https://neckpinch.com/authors/thibaut-delcroix/New arXiv papers by Thibaut Delcroix, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1911.08300/arxiv:1911.08300Tue, 19 Nov 2019 00:00:00 GMTThibaut 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 quadric along a linear subquadric admits Kähler-Einstein metrics, providing infinitely many examples of manifolds with no Kähler-Ricci solitons that are not K-semistable. Using a different construction, we provide an infinite family of Fano manifolds with no Kähler-Einstein metrics but which admit coupled Kähler-Einstein metrics. Finally, we elaborate on the relationship between Kähler-Ricci solitons and the more general concept of multiplier Hermitian structures and illustrate this with examples related to the two previous families.Ricci solitonsKähler–Ricci solitonsEinstein metricsSingularitiesKähler geometryStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/1812.07218/arxiv:1812.07218Tue, 18 Dec 2018 00:00:00 GMTThibaut 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 necessary and sufficient conditions for existence of coupled Kähler-Ricci solitons, Mabuchi metrics and twisted Kähler-Einstein metrics in terms of combinatorial data of the manifold.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stability https://neckpinch.com/papers/1608.01852/arxiv:1608.01852Fri, 05 Aug 2016 00:00:00 GMTThibaut Delcroix — We prove a criterion for K-stability of a ℚ-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano manifolds proved by Datar and Székelyhidi, it yields a criterion for the existence of a Kähler-Einstein metric on a spherical Fano manifold. The results hold also for modified K-stability and existence of Kähler-Ricci solitons.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability