9 papers
Commensurability Relations Between Deligne-Mostow-Thurston and Ghazouani-Pirio Monodromy Groups
Chenglong Yu, Yiming Zhong
We classify commensurability relations between Deligne--Mostow--Thurston monodromy groups and the sixteen arithmetic Ghazouani--Pirio monodromy groups arising from moduli of flat c…
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…
Double integrals and transformation formulas for Appell--Lauricella hypergeometric functions
Shihao Wang, Chenglong Yu, Zhiwei Zheng
The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations amo…
Rigidity Criterion for Certain Calabi-Yau Families
Ruiran Sun, Chenglong Yu, Kang Zuo
We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. If, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, a…
Homology of Local Systems on Real Line Arrangement Complements
Baiting Xie, Chenglong Yu
We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establis…
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…
Deformations of highly symmetric Calabi-Yau Grassmannian hypersurfaces
Adriana Salerno, Ursula Whitcher, Chenglong Yu
We use arithmetic and Hodge-theoretic techniques to study pencils of Calabi-Yau varieties realized as highly symmetric hypersurfaces in Grassmannians and their quotients, demonstra…
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…