https://neckpinch.com/authors/abdellah-lahdili/New arXiv papers by Abdellah Lahdili, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2412.02564/arxiv:2412.02564Tue, 03 Dec 2024 00:00:00 GMTVestislav Apostolov, Abdellah Lahdili, Eveline Legendre — We show that if X is a smooth Fano manifold which caries a Kähler Ricci soliton, then the canonical cone of the product of X with a complex projective space of sufficiently large dimension is a Calabi–Yau cone. This can be seen as an asymptotic version of a conjecture by Mabuchi and Nikagawa. This result is obtained by the openness of the set of weight functions v over the momentum polytope of a given smooth Fano manifold, for which a v-soliton exists. We discuss other ramifications of this approach, including a Licherowicz type obstruction to the existence of a Kähler Ricci soliton and a Fujita type volume bound for the existence of a v-soliton.Ricci solitonsKähler–Ricci solitonsRicci-flat & Calabi–YauKähler geometryKähler–Einstein & K-stability https://neckpinch.com/papers/2408.06267/arxiv:2408.06267Mon, 12 Aug 2024 00:00:00 GMTMichael Hallam, Abdellah Lahdili — We introduce a new weighted version of the Hermite–Einstein equation, along with notions of weighted slope (semi/poly)stability, and prove that a vector bundle admits a weighted Hermite–Einstein metric if and only if it is weighted slope polystable. The new equation encompasses several well-known examples of canonical Hermitian metrics on vector bundles, including the usual Hermite–Einstein metrics, Kähler–Ricci solitons, and transversally Hermite–Einstein metrics on certain Sasaki manifolds. We prove that the equation arises naturally as a moment map, that solutions to the equation are unique up to scaling, and demonstrate a weighted Kobayashi–Lübke inequality satisfied by vector bundles admitting a weighted Hermite–Einstein metric. As an application of our techniques, we extend a bound of Tian on the Ricci curvature to a bound on a modified Ricci curvature, related to the existence of Kähler–Ricci solitons. Along the way, we introduce a new weighted vortex equation, as well as a weighted analogue of Gieseker stability. A key technical point is the application of a new extension of Inoue's equivariant intersection numbers to arbitrary weight functions on the moment polytope of a Kähler manifold with Hamiltonian torus action.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryStability & uniquenessSasakian & contact geometry