https://neckpinch.com/authors/carlos-esparza/New arXiv papers by Carlos Esparza, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.03592arxiv:2610.03592Fri, 02 Oct 2026 00:00:00 GMTCarlos Esparza, Junsheng Zhang — For noncompact smooth Kähler-Ricci shrinkers, we prove a Matsushima theorem identifying the centralizer of the soliton field with the complexification of its Killing centralizer, uniqueness up to biholomorphism on a fixed complex manifold, and K-polystability of the associated polarized Fano fibration.Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compactKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2512.03323arxiv:2512.03323Wed, 03 Dec 2025 00:00:00 GMTCharles Cifarelli, Carlos Esparza — Recently, Sun-Zhang have developed an algebraic theory for Kähler-Ricci shrinkers showing that they admit the structure of a polarized Fano fibration (π: X → Y, ξ). In particular, they conjecture that existence of a Kähler-Ricci shrinker metric is equivalent to a notion of K-stability. We prove one direction of this conjecture, namely that existence of a Kähler-Ricci shrinker metric g implies K-polystability of (π: X → Y, ξ), in the case that the Ricci curvature of g decays at infinity. As an application, we give a non-existence result: if M is the blowup of a six-dimensional quadric along a two-dimensional subquadric, then the total space X of the cube root of K_M is a polarized Fano fibration not admitting a Kähler-Ricci shrinker.Ricci solitonsSingularitiesSurfacesKähler geometryStability & uniquenessBoundaries & non-compactKähler–Einstein & K-stabilityAnalytic minimal model program https://arxiv.org/abs/2503.05838arxiv:2503.05838Thu, 06 Mar 2025 00:00:00 GMTCarlos Esparza — We show that smooth polarized Fano fibrations have no nontrivial finite covers. Using results by Sun-Zhang and Wylie, it follows that shrinking Kähler-Ricci solitons are simply-connected.Ricci solitonsKähler–Ricci solitonsKähler geometryAnalytic minimal model program https://arxiv.org/abs/2502.13521arxiv:2502.13521Wed, 19 Feb 2025 00:00:00 GMTCarlos Esparza — We show that, up to biholomorphism, a given noncompact complex manifold only admits one shrinking gradient Kähler-Ricci soliton with Ricci curvature tending to zero at infinity. Our result does not require fixing the asymptotic data of the metric, nor fixing the soliton vector field. The method used to prove the uniqueness of the soliton vector field can be applied more widely, for example to show that conical Calabi-Yau metrics on a given complex manifold are unique up to biholomorphism. We also use it to prove that if two polarized Fano fibrations, as introduced by Sun-Zhang, are biholomorphic, then they are isomorphic as algebraic varieties.Ricci solitonsKähler–Ricci solitonsRicci-flat & Calabi–YauKähler geometryStability & uniquenessBoundaries & non-compactAnalytic minimal model program