5 citations · 8 across the 8 of their papers we have counts for
9 papers · 1 filter
A non-holomorphic P=W phenomenon
Zili Zhang
We prove the P=W identity for isolated cluster varieties of dimension 3 without the full rank hypothesis. These cluster varieties are generally singular, and the associated Lagrang…
Mixed Hodge Structures of cluster varieties of dimension 3
Yuhang Zhang, Zili Zhang
We calculate the mixed Hodge numbers of smooth 3-dimensional cluster varieties and show that they are of mixed Tate type. We also study the mixed Hodge structures of the cohomology…
Local multiplicativity of perverse filtrations
Zili Zhang
Let be a proper surjective morphism from a smooth Kähler surface to a smooth curve. We show that the local perverse filtration associated with the induced map $S^{[n]}\t…
The identity for isolated cluster varieties: full rank case
Zili Zhang
We initiate a systematic construction of real analytic Lagrangian fibrations from integer matrices. We prove that when the matrix is of full column rank, the perverse filtration as…
Perverse filtration for generalized Kummer varieties of fibered surfaces
Zili Zhang
Let be a proper surjective morphism from a smooth connected quasi-projective commutative group scheme of dimension 2 to a smooth curve. The construction of generalized Kum…
Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces, II
Zili Zhang
Let be a smooth quasi-projective surface properly fibered onto a smooth curve. We prove that the multiplicativity of the perverse filtration on a…
The identity for cluster varieties
Zili Zhang
We find new examples of the identity of de Cataldo-Hausel-Migliorini by studying cluster varieties. We prove that the weight filtration of 2D cluster varieties correspond to…
Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles
Junliang Shen, Zili Zhang
We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams , , $\tilde{E}_…
Multiplicativity of Perverse Filtration for Hilbert Schemes of Fibered Surfaces
Zili Zhang
Let be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to…