6 papers · 1 filter
On bicanonical maps of threefolds of general type with large volumes
Chen Jiang, Ziqi Liu
We prove that for any smooth projective -fold of general type with canonical volume greater than , the image of its bicanonical map has dimension at least . We also stu…
A canonical Fano threefold has Fano index
Chen Jiang, Haidong Liu
We show that the -Fano index of a canonical weak Fano -fold is at most . This upper bound is optimal and gives an affirmative answer to a conjecture of Chengxi W…
Numerical invariants of hyper-Kähler manifolds
Olivier Debarre, Chen Jiang
We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler manifolds, mostly in dimension 6 and in the presence of an…
An effective upper bound for Fano indices of canonical Fano threefolds, I
Chen Jiang, Haidong Liu
Let be a -factorial weak Fano -fold with at worst isolated canonical singularities. We show that the -Fano index of is at most .
Total Cartier index of a bounded family
Jingjun Han, Chen Jiang
We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.
Optimal upper bound for degrees of canonical Fano threefolds of Picard number one
Chen Jiang, Haidong Liu, Jie Liu
We show that for a -factorial canonical Fano -fold of Picard number , . The main tool is a Kawamata--Miyaoka type inequality which relates $(-…