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Jungkai Chen

Publications and source records attributed to Jungkai Chen.

4 recordsLinked to original sources
arXiv2026

Deformation of pairs of $\mathbb{P}^3$ and hypersurfaces

Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the classification of $\mathbb{Q}$-Gorenstein degenerations of $\mathbb{P}^3$ with canonical singularities. We prove that if a degenerating threefold has canonical singularities, then the moduli space is smooth at the corresponding pair. Consequently, we find some boundary divisors of the moduli of smooth hypersurfaces. Finally, using the double cover method, we derive some information on the moduli space of threefolds $X$ with canonical singularities with the same volume and geometric genus as a double cover of $\mathbb{P}^3$ branched over a hypersurface.

math.AG↗
arXiv2020

Addendum to "The Noether inequality for algebraic threefolds"

In this short note, we give a refinement of our previous work (arXiv:1803.05553) stating that for a projective $3$-fold $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 11$, $$\text{vol}(X)\geq \frac{4}{3}p_g(X)-{\frac{10}{3}}.$$

math.AG↗
arXiv2016

Irregular varieites with geometric genus one, theta divisors, and fake tori

We study the Albanese image of a compact Kähler manifold whose geometric genus is one. We prove that if the Albanese map is not surjective, then the manifold maps surjectively onto an ample divisor in some abelian variety, and in many cases the ample divisor is a theta divisor. With a further natural assumption on the topology of the manifold, we prove that the manifold is an algebraic fiber space over a genus two curve. Finally we apply these results to study the geometry of a compact Kähler manifold which has the same Hodge numbers as those of an abelian variety of the same dimension.

math.AG↗