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math.AG2022
On general type varieties admitting global holomorphic forms
Meng Chen, Zhi Jiang
For all nonsingular projective -folds of general type, we prove the existence of Noether type inequalities in the following form: $$\text{vol}(V)\geq a_{n,k}h^0(Ω_V^k)-b_{n,…
math.AG2022
Angehrn-Siu-Helmke's method applied to abelian varieties
Zhi Jiang
We apply Angehrn-Siu-Helmke's method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for ve…
math.AG2022
G-stable rank of symmetric tensors and log canonical threshold
Zhi Jiang
Shitov recently gave a counterexample to Comon's conjecture that the symmetric tensor rank and tensor rank of a symmetric tensor are the same. In this paper we show that an analog…