https://neckpinch.com/authors/eveline-legendre/New arXiv papers by Eveline Legendre, 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