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All Outputs (4)

One-dimensional components in the K-moduli of smooth Fano 3-folds (2024)
Journal Article
Abban, H., Cheltsov, I., Denisova, E., Etxabarri Alberdi, E., Kaloghiros, A.-S., Jiao, D., Martinez Garcia, J., & Papazachariou, T. (2024). One-dimensional components in the K-moduli of smooth Fano 3-folds. Journal of Algebraic Geometry, https://doi.org/10.1090/jag/839+

By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of smoothable Fano 3-folds.

On K-moduli of quartic threefolds (2024)
Journal Article
Abban, H., Cheltsov, I., Kasprzyk, A., Liu, Y., & Petracci, A. (in press). On K-moduli of quartic threefolds. Algebraic Geometry,

The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octic surface. They can all be parametrised as complete intersections of a... Read More about On K-moduli of quartic threefolds.

Seshadri constants and K-stability of Fano manifolds (2023)
Journal Article
Abban, H., & Zhuang, Z. (2023). Seshadri constants and K-stability of Fano manifolds. Duke Mathematical Journal, 172(6), 1109-1144. https://doi.org/10.1215/00127094-2022-0026

We give a lower bound of the ı-invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of Fano hypersurfaces of arbitrarily large index, as well as the uniform K-s... Read More about Seshadri constants and K-stability of Fano manifolds.