Yuchen Liu

Characterization of projective spaces by Seshadri constants

We prove that an n-dimensional complex projective variety is isomorphic to

Construction of hyperbolic Horikawa surfaces

{\mathbb {P}}^n

K\"ahler-Einstein metrics and volume minimization

Pn if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n. We also classify complex projective varieties with Seshadri constants equal to n.

K-stability of cubic threefolds

We prove that a cyclic cover of a smooth complex projective variety is Brody hyperbolic if its branch divisor is a generic small deformation of a large enough multiple of a Brody hyperbolic base-point-free ample divisor. We also show the hyperbolicity of complements of those branch divisors. As an application, we find new examples of Brody hyperbolic hypersurfaces in

A Guided Tour to Normalized Volume

\mathbb{P}^{n+1}

Openness of uniform K-stability in families of

that are cyclic covers of

\mathbb{Q}

\mathbb{P}^n

-Fano varieties

.