9 citations · 31 across the 15 of their papers we have counts for
17 papers
A Sharp Bound for the Second Betti Number of Hyperkähler Sixfolds
Jie Fu, Bin Wang, Shihao Wang +1
Let be a smooth compact irreducible hyperkähler manifold of dimension six. We prove that the second Betti number satisfies . Furthermore, we show that the third…
Classification of Automorphism Groups of Smooth Cubic Threefolds and Fourfolds
Jie Fu, Shihao Wang, Zhiwei Zheng
We classify the automorphism groups of smooth cubic threefolds and fourfolds. We also show that there are (respectively, ) connected families of smooth cubic fourfolds (r…
Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory
Jie Fu, Zhiwei Zheng
Laza and the second author have classified all possible symplectic automorphism groups of smooth cubic fourfolds. There are such groups, and by Koike, there are families…
Monodromy Eigenvalues of Milnor Fibers for Line Arrangements
Baiting Xie, Chenglong Yu, Zhiwei Zheng
It is an important problem to know whether the monodromy on the cohomology of Milnor fibers associated to hyperplane arrangements is a combinatorial invariant. In this paper, we ob…
Sylow Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces
Baiting Xie, Zhiwei Zheng
In this paper, we first establish Sylow criteria for liftability of finite subgroups of the projective linear groups over arbitrary field. We also obtain Sylow criteria for -lif…
Non-symplectic Indices of Automorphism Groups of Smooth Cubic Fourfolds
Jie Fu, Shihao Wang, Zhiwei Zheng
We study the full automorphism groups of smooth cubic fourfolds with prescribed symplectic automorphism group. Our starting point is the classification of symplectic automorphism g…
Moduli spaces of sextic curves with simple singularities and their compactifications
Chenglong Yu, Zhiwei Zheng, Yiming Zhong
In this paper, we study moduli spaces of sextic curves with simple singularities. Through period maps of K3 surfaces with ADE singularities, we prove that such moduli spaces admit…
Commensurability Among Deligne-Mostow Monodromy Groups
Chenglong Yu, Zhiwei Zheng
This paper gives the commensurability classification of Deligne--Mostow ball quotients and shows that the 104 Deligne--Mostow lattices form 38 commensurability classes. First, we f…
Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces
Chenglong Yu, Zhiwei Zheng
In this paper we mainly study Calabi--Yau varieties that arise as triple covers of products of projective lines branched along simple normal crossing divisors. For some of those fa…
Degenerations to secant cubic hypersurfaces and limiting Hodge structure
Renjie Lyu, Zhiwei Zheng
The secant variety of the Veronese surface is a singular cubic fourfold. Degenerations to this specific cubic fourfold and the associated limiting Hodge structures are key ingredie…
The Complex Ball-quotient Structure of the Moduli Space of Certain Sextic Curves
Zhiwei Zheng, Yiming Zhong
We study moduli spaces of certain sextic curves with a singularity of multiplicity 3 from both perspectives of Deligne-Mostow theory and periods of K3 surfaces. In both ways we can…
Abelian Automorphism Groups of Quartic Surfaces and Cubic Fourfolds
Tianzhen Peng, Zhiwei Zheng
In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable a…
On Abelian Automorphism Groups of Hypersurfaces
Zhiwei Zheng
Given integers and . Let be a finite abelian group acting faithfully and linearly on a smooth hypersurface of degree in the complex projective space $\math…
Automorphisms and Periods of Cubic Fourfolds
Radu Laza, Zhiwei Zheng
We classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sub…
Moduli of Nodal Sextic Curves via Periods of K3 Surfaces
Chenglong Yu, Zhiwei Zheng
In this paper we study the moduli spaces of nodal sextic curves. We realize each irreducible component of the GIT space of sextic curves with given number of nodes as an open subsp…
Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties
Chenglong Yu, Zhiwei Zheng
In this paper we realize the moduli spaces of cubic fourfolds with specified automorphism groups as arithmetic quotients of complex hyperbolic balls or type IV symmetric domains, a…
Orbifold Aspects of Certain Occult Period Maps
Zhiwei Zheng
We first characterize the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds. Then we determine for some complex projective manifolds of small dimensio…