4 papers
A Matsushima theorem, uniqueness and K-polystability for Kähler-Ricci shrinkers
Carlos 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, u…
K-polystability of Asymptotically Conical Kähler-Ricci Shrinkers
Charles 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 . In particul…
Shrinking gradient Kähler-Ricci solitons are simply-connected
Carlos 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-con…
Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons
Carlos 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. Ou…