37 citations · 362 across the 39 of their papers we have counts for
5 papers · 1 filter
Multiplicity free gradings on semisimple Lie and Jordan algebras and skew root
Gang Han, Kang Lu, Yucheng Liu
A -grading on an algebra is called multiplicity free if each homogeneous component of the grading is 1-dimensional, where is an abelian group. We introduce skew root systems…
Characterization of projective spaces by Seshadri constants
Yuchen Liu, Ziquan Zhuang
We prove that an -dimensional complex projective variety is isomorphic to if the Seshadri constant of the anti-canonical divisor at some smooth point is greater t…
The volume of singular Kähler-Einstein Fano varieties
Yuchen Liu
We show that the anti-canonical volume of an -dimensional Kähler-Einstein -Fano variety is bounded from above by certain invariants of the local singularities, namel…
Kähler-Einstein metrics and volume minimization
Chi Li, Yuchen Liu
We prove that if a -Fano variety specially degenerates to a Kähler-Einstein -Fano variety , then for any ample Cartier divisor with $…
Hyperbolicity of cyclic covers and complements
Yuchen Liu
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 h…