Seshadri constants and K-stability of Fano manifolds

22 Jan 2021 · Hamid Abban, Ziquan Zhuang ·

We give a lower bound of the $\delta$-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-stability of most families of smooth Fano threefolds of Picard number one.