8 papers
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…
An upper bound for polynomial volume growth of automorphisms of zero entropy
Fei Hu, Chen Jiang
Let be a normal projective variety of dimension over an algebraically closed field and an automorphism of . Suppose that the pullback $f^*|_{\mathsf{N}^1(X)_\mathbf{…
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 $(-…
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…
The Noether inequality for threefolds and three moduli spaces with minimal volumes
Meng Chen, Yong Hu, Chen Jiang
We establish the Noether inequality \[\textrm{Vol}(X)\geq \frac{4}{3}p_g(X)-\frac{10}{3}\] for all projective -folds of general type with geometric genus $5\leq p_g(X)\leq 1…
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…