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Xueqing Wen

Publications and source records attributed to Xueqing Wen.

9 recordsLinked to original sources
arXiv2026

Spaltenstein Varieties Associated with Pseudo-Polarizations

We introduce minimal Richardson orbits and pseudo-polarizations for nilpotent orbits in classical Lie algebras of types B, C, and D. For any nilpotent orbit, we classify all minimal Richardson orbits containing it and thereby determine the associated pseudo-polarizations. We prove that the corresponding Spaltenstein varieties are smooth and pure dimensional, with iterated orthogonal/isotropic Grassmannian fibrations. As an application, we extend the seesaw property and duality of Fu-Ruan-Wen from Richardson orbits to all special orbits in types B and C.

math.AG↗
arXiv2026

Minimal reduction type in classical cases

We prove Yun's minimal reduction conjecture for all classical groups. More precisely, for any topologically nilpotent regular semisimple element $γ$, we show that the associated minimal reduction set $\mathrm{RT}_{\mathrm{min}}(γ)$ consists of a single nilpotent orbit. This result confirms and extends Yun's earlier work in types A and C, and resolves the remaining cases in types B and D. Moreover, we provide an explicit and effective procedure for determining $\mathrm{RT}_{\mathrm{min}}(γ)$.

math.AG↗
arXiv2025

Springer correspondence and mirror symmetries for parabolic Hitchin systems

We prove the Strominger--Yau--Zaslow and topological mirror symmetries for parabolic Hitchin systems of types B and C. In contrast to type A, a geometric reinterpretation of Springer duality is necessary. Furthermore, unlike Hitchin's construction in the non-parabolic case, the map between generic fibers in type B and C needs more analysis due to the change of partitions of Springer dual nilpotent orbits, which is the main difficulty in this article. To tackle this challenge, we first construct and study the geometry of the generic Hitchin fibers of moduli spaces of Higgs bundles associated to the nilpotent orbit closures. Then we study their relation with the generic Hitchin fibers of parabolic Hitchin systems. Along this way, we establish intriguing connections between Springer duality, Kazhdan--Lusztig maps, and singularities of spectral curves, and uncover a new geometric interpretation of Lusztig's canonical quotient.

math.AG↗
arXiv2025

On the generic fibers and true base of parabolic $\mathrm{SO}_{2n}$-Hitchin systems

In this paper, we confirm a physical conjecture regarding the parabolic $\mathrm{SO}_{2n}$-Hitchin system, showing that Hitchin map factors through a finite cover of the Hitchin base that is isomorphic to an affine space. We first show that the generic Hitchin fiber is disconnected, with the number of components determined by the degree of the generalized Springer map, and then construct the cover explicitly. To this end, we introduce and study a new class of moduli spaces, termed \emph{residually nilpotent Hitchin systems}, and analyze their generic Hitchin fibers. Furthermore, we uncover an interesting connection between self-duality of the generic Hitchin fiber and special nilpotent orbits.

math.AG↗
arXiv2022

Topological Mirror Symmetry of Parabolic Hitchin Systems

In this paper, we first prove the parabolic Beauvile-Narasimhan-Ramanan correspondence over an arbitrary field which generalizes the corresponding results over algebraically closed fields in [SWW22]. We use the correspondence and the p-adic integration methods developed by Groechenig- Wyss-Ziegler [GWZ20b] to prove the topological mirror symmetry for parabolic Hitchin systems on curves with arbitrary parabolic structures.

math.AG↗
arXiv2021

Parabolic Hitchin Maps and Their Generic Fibers

We set up a BNR correspondence for moduli spaces of Higgs bundles over a curve with a parabolic structure over any algebraically closed field. This leads to a concrete description of generic fibers of the associated strongly parabolic Hitchin map. We also show that the global nilpotent cone is equi-dimensional with half dimension of the total space. As a result, we prove the flatness and surjectivity of this map and the existence of very stable parabolic vector bundles.

math.AG↗
arXiv2021

On the moduli spaces of parabolic symplectic orthogonal bundles on curves

We prove that the moduli spaces of parabolic symplectic/orthogonal bundles on a smooth curve are globally F regular type. As a consequence, all higher cohomology of theta line bundle vanish. During the proof, we develop a method to estimate codimension, and consider the infinite grassmannians for parabolic $G$ bundles.

math.AG↗