17 citations · 75 across the 24 of their papers we have counts for
26 papers
Quasi-Projectivity of Weighted Right-Angled Artin Groups
Yongqiang Liu, Xiaobin Xu
Weighted right-angled Artin groups generalize right-angled Artin groups by adding weights to the edges of the defining graphs. We classify the weighted right-angled Artin groups th…
Spectral sequences, Massey products and homology of covering spaces
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We revisit the equivariant spectral sequence considered by Papadima-Suciu, and show that all its differentials are computed by higher order Massey products. As a first application,…
Maximal twisted Betti numbers of complex hyperplane arrangement complements
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We show that the Betti numbers of a local system on the complement of an essential complex hyperplane arrangement are maximized precisely when the local system is constant. This re…
Brylinski-Radon transformation and generic projections
Yongqiang Liu, Laurentiu Maxim, Botong Wang
Using the Brylinski-Radon transformation, we prove that under a generic surjective linear map from C^n to C^m, the pushforward of a perverse sheaf is perverse, modulo shifts of con…
Cohomology of -local systems on complex hyperplane arrangement complements
Yongqiang Liu, Laurenţiu Maxim, Botong Wang
We prove a Cohen-Dimca-Orlik type theorem for rank one -local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S. Sugawara.
-type invariants and cohomology jump loci for complex smooth quasi-projective varieties
Fenglin Li, Yongqiang Liu
Let X be a complex smooth quasi-projective variety with a fixed epimorphism . In this paper, we consider the asymptotic behaviour of inv…
Non-abelian Mellin Transformations and Applications
Yongqiang Liu, Laurenţiu Maxim, Botong Wang
We study non-abelian versions of the Mellin transformations, originally introduced by Gabber-Loeser on complex affine tori. Our main result is a generalization to the non-abelian c…
Generic Vanishing, 1-forms, and Topology of Albanese Maps
Yajnaseni Dutta, Feng Hao, Yongqiang Liu
Given a bounded constructible complex of sheaves on a complex Abelian variety, we prove an equality relating the cohomology jump loci of and its singula…
Cohomological connectivity of perturbations of map-germs
Yongqiang Liu, Guillermo Peñafort Sanchis, Matthias Zach
Let be a finite map-germ with and the image of a small perturbation . We show that the reduced cohomology of is…
The deletion restriction method for plane curve germ complement
Yongqiang Liu
We study the cohomology jump loci of rank one local systems for the plane curve germ complement by the deletion restriction method. In particular, the deletion restriction type res…
Aspherical manifolds, Mellin transformation and a question of Bobadilla-Kollár
Yongqiang Liu, Laurenţiu Maxim, Botong Wang
In their 2012 paper, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibrati…
Length of Perverse Sheaves on Hyperplane Arrangements
Nero Budur, Yongqiang Liu
In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over a…
Perverse sheaves on semi-abelian varieties -- a survey of properties and applications
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various obstructions on the homotopy type of complex…
Perverse sheaves on semi-abelian varieties
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on…
Mellin transformation, propagation, and abelian duality spaces
Yongqiang Liu, Laurentiu Maxim, Botong Wang
For arbitrary field coefficients , we show that -perverse sheaves on a complex affine torus satisfy the so-called propagation package, i.e., the generic van…
On the length of perverse sheaves and D-modules
Nero Budur, Pietro Gatti, Yongqiang Liu +1
We prove that the length function for perverse sheaves and algebraic regular holonomic D-modules on a smooth complex algebraic variety Y is an absolute Q-constructible function. On…
Milnor and Tjurina numbers for a hypersurface germ with isolated singularity
Yongqiang Liu
Assume that is an analytic function germ at the origin with only isolated singularity. Let and be the corresponding Milnor and Tjuri…
Generic vanishing for semi-abelian varieties and integral Alexander modules
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological applications. In particula…
Topology of subvarieties of complex semi-abelian varieties
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We use the non-proper Morse theory of Palais-Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties, and that of their infinite cyclic co…
The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties
Nero Budur, Yongqiang Liu, Botong Wang
Given any connected topological space , assume that there exists an epimorphism . The deck transformation group acts on the associated inf…
Spectral pairs, Alexander modules, and boundary manifolds
Yongqiang Liu, Laurentiu Maxim
Let $f: \CN \rightarrow \C $ be a reduced polynomial map, with , $\U=\CN \setminus D$ and boundary manifold $M=\partial \U$. Assume that is transversal at infinity…
Cohomology support loci of local systems
Nero Budur, Yongqiang Liu, Luis Saumell +1
The support S of Sabbah's specialization complex is a simultaneous generalization of the set of eigenvalues of the monodromy on Deligne's nearby cycles complex, of the support of t…
The total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial
Yongqiang Liu
We give a concrete formula for the total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial in most of the interesting cases. As an application, we give a description o…
Characteristic Varieties of Hypersurface Complements
Yongqiang Liu, Laurentiu Maxim
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of t…