K-stability for Fano manifolds with torus action of complexity $1$
By Nathan Owen Ilten, Hendrik Suss. 2015
60 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b871356266f00d9be07b828787617523bed98248
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In Applied Mathematics
- Chi Li
- Jiyuan Han
- G'abor Sz'ekelyhidi
- Thibaut Delcroix
- Tristan C. Collins
- Chenyang Xu
- Yuchen Liu
- Xiaowei Wang
In Geometry and Topology
- Chi Li
- Jiyuan Han
- G'abor Sz'ekelyhidi
- Thibaut Delcroix
- Tristan C. Collins
- Chenyang Xu
- Yuchen Liu
- Xiaowei Wang
Citations in the corpus
- Sasaki–Einstein metrics and K–stability (2015, methodology): “ s. This new p-divisor only has two distinct polytopes, and so from the description of T-equivariant test configurations with normal 56 T.C. COLLINS AND G. SZEKELYHIDI´ central fiber due to Ilten-Suss [52] we see that there are at most two nontrivial test configurations. The same applies when bm q is a”
- K-stability of Fano spherical varieties (2016, methodology): “here an analogue of the Yau-Tian-Donaldson conjecture was obtained by Collins and Székelyhidi [CS]. Finally, it would be interesting to combine the ideas from our work with the work of Ilten and Süss [IS17] to study varieties with a spherical action of complexity one. In particular, Langlois and Ter”
- On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “ndition g >0, which we assumed, becomes an obstruction to the existence of the corresponding equation. More generally, the similar applications can be applied to T-varieties of complexity one (see [23, 46]) and spherical varieties as in [29] or Fano G-varieties (for a reductive complex Lie group ”