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Jiabin Du

Publications and source records attributed to Jiabin Du.

5 recordsLinked to original sources
arXiv2026

On the canonical degree of a Gorenstein minimal threefold of general type

Let $X$ be a Gorenstein minimal $3$-fold of general type whose canonical map is generically finite. We prove that if $p_g(X)> 243$, then the degree of the canonical map is at most $72$. Moreover, equality holds only if the general fibre $F$ of the Albanese morphism of $X$ is a smooth minimal surface of general type satisfying $p_g(F)=3,q(F)=0$ and $K_F^2=36$, and the canonical map of $F$ has degree $36$. This result improves the lower bound on $p_g(X)$ previously obtained by Jin-Xing Cai~\cite{Cai08}. As a consequence, we show that if the canonical degree is bigger than $64$, then the general fibre of the Albanese morphism of $X$ is a surface with irregularity zero.

math.AG↗
arXiv2026

Geometry of Holomorphic One-forms on Smooth Projective Varieties

In this article, we show that any morphism $f$ from a smooth projective variety $X$ to a simple abelian variety $A$ is smooth, if and only if there exists a holomorphic 1-form $\omega$ on $A$ such that $f^*\omega$ has no zero. As the key ingredient in the proof, we show any $\mathbb{Z}$-homology fibre bundle morphism is without blow-up in codimension 0 in the sense of Sabbah. Furthermore, we investigate the structure of the spaces of holomorphic 1-forms with zeros, and show that they are linear for large classes of varieties. Also, we construct a delicate example of a smooth projective subvariety of an abelian variety for which the holomorphic 1-forms with positive dimensional zero loci do not form a linear subset. Finally, we study algebraic surfaces admitting holomorphic 1-forms that have zeros and do not arise from cohomology jump loci.

math.AG↗
arXiv2025

On symplectic automorphisms of a surface with genus two fibration and their action on $\mathrm{CH}_0$

Let $S$ be a complex smooth projective surface with a genus two fibration, and $\mathrm{Aut}_s(S)$ the group of symplectic automorphisms, fixing every holomorphic 2-forms (if any) on $S$. Based on the work of Jin-Xing Cai, we observe in this paper that, if $\chi(\mathcal{O}_S)\geq 5$, then $|\mathrm{Aut}_s(S)|\leq 2$. Then we go on to verify, under some conditions, that $\mathrm{Aut}_s(S)$ acts trivially on the Albanese kernel $\mathrm{CH}_0(S)_{\mathrm{alb}}$ of the 0-th Chow group, which is predicted by a conjecture of Bloch and Beilinson. As a consequence, if an automorphism $\sigma\in \mathrm{Aut}(S)$ acts trivially on $H^{i,0}(S)$ for $0\leq i\leq 2$, then it also acts trivially on $\mathrm{CH}_0(S)_{\mathrm{alb}}$.

math.AG↗
arXiv2022

On symplectic automorphisms of elliptic surfaces acting on $\mathrm{CH}_0$

Let $S$ be a complex smooth projective surface of Kodaira dimension one. We show that the group $\mathrm{Aut}_s(S)$ of symplectic automorphisms acts trivially on the Albanese kernel $\mathrm{CH}_0(S)_\mathrm{alb}$ of the $0$-th Chow group $\mathrm{CH}_0(S)$, unless possibly if the geometric genus and the irregularity satisfy $p_g(S)=q(S)\in\{1,2\}$. In the exceptional cases, the image of the homomorphism $\mathrm{Aut}_s(S)\rightarrow \mathrm{Aut}(\mathrm{CH}_0(S)_\mathrm{alb})$ has order at most 3. Our arguments actually take care of the group $\mathrm{Aut}_f(S)$ of fibration-preserving automorphisms of elliptic surfaces $f\colon S\rightarrow B$. We prove that, if $σ\in\mathrm{Aut}_f(S)$ induces the trivial action on $H^{i,0}(S)$ for $i>0$, then it induces the trivial action on $\mathrm{CH}_0(S)_\mathrm{alb}$. As a by-product we obtain that if $S$ is an elliptic K3 surface, then $\mathrm{Aut}_f(S)\cap \mathrm{Aut}_s(S)$ acts trivially on $\mathrm{CH}_0(S)_\mathrm{alb}$.

math.AG↗