K-Stability for Fano Manifolds with Torus Action of Complexity One
Nathan Ilten, Hendrik S\"u{\ss}
TL;DR
This paper investigates Fano manifolds with a one-codimension torus action, using equivariant K-stability to identify the existence of Kahler-Ricci solitons and providing new examples of Kahler-Einstein Fano threefolds.
Contribution
It applies recent theoretical results to effectively determine Kahler-Ricci solitons on specific Fano manifolds with torus actions, expanding known examples.
Findings
New examples of Kahler-Einstein Fano threefolds identified.
Existence of Kahler-Ricci solitons established for certain Fano manifolds.
Effective criteria for K-stability in the presence of torus actions.
Abstract
We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds, and Fano threefolds admitting a non-trivial Kahler-Ricci soliton.
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