arXiv subjects

Jia Choon Lee

Publications and source records attributed to Jia Choon Lee.

6 recordsLinked to original sources

arXiv2026

Symplectic leaves of meromorphic Hitchin systems

The moduli space of meromorphic Higgs bundles admits a Poisson structure due to the independent work of Bottacin and Markman. In this paper, we revisit the symplectic leaves of this Poisson structure for the tame case. We study the partial compactification of the restricted Hitchin map on the symplectic leaves to an algebraically completely integrable system. In particular, we show that such a partial compactification is realized by the moduli spaces of $\vecξ$-parabolic Higgs bundles. These same moduli spaces also provide a symplectic resolution of the normalization of the closure of the corresponding symplectic leaves. Finally, we discuss connectedness results for the corresponding Betti moduli spaces under the tame non-abelian Hodge correspondence.

math.AG↗

arXiv2026

Spectral correspondence for cyclic Higgs bundles

In this paper, we describe the spectral correspondence for cyclic Higgs bundles from the viewpoint of quiver bundles. Under this framework, we establish a one-to-one correspondence between cyclic Higgs bundles on a curve and sheaves on a noncommutative surface whose noncommutative structure originates from the path algebra associated to the cyclic quiver. As applications, this correspondence generalizes the known spectral correspondence for $U(p,p)$-Higgs bundles and establish a connection between the spectral data for $U(p,q)$-Higgs bundles and modules over the sheaf of even Clifford algebras of a conic fibration.

math.AG↗

arXiv2025

Relative spectral correspondence for parabolic Higgs bundles and Deligne--Simpson problem

In this paper, we generalize the spectral correspondence for parabolic Higgs bundles established by Diaconescu--Donagi--Pantev to the relative setting. We show that the relative moduli space of $\vecξ$-parabolic Higgs bundles on a curve can be realized as the relative moduli space of pure dimension one sheaves on a family of holomorphic symplectic surfaces. This leads us to formulate the image of the relative moduli space under the Hitchin map in terms of linear systems on the family of surfaces. Then we explore the relationship between the geometry of these linear systems and the so-called $OK$ condition introduced by Balasubramanian--Distler--Donagi in the context of six-dimensional superconformal field theories. As applications, we obtain (a) the non-emptiness of the moduli spaces and (b) the Deligne--Simpson problem and its higher genus analogue. In particular, we prove a conjecture proposed by Balasubramanian--Distler--Donagi that the $OK$ condition is sufficient for solving the Deligne--Simpson problem.

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arXiv2024

Generators for the cohomology of the moduli space of irregular parabolic Higgs bundles

We prove that the pure part of the cohomology ring of the moduli space of irregular $\underlineξ$-parabolic Higgs bundles is generated by the Künneth components of the Chern classes of a universal bundle and the Chern classes of the successive quotients of a universal flag of subbundles. As an application, in the regular full-flag case, we demonstrate a similar result for the cohomology ring of the moduli spaces of parabolic and strongly parabolic Higgs bundles.

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arXiv2023

Moduli spaces of modules over even Clifford algebras and Prym varieties

A conic fibration has an associated sheaf of even Clifford algebras on the base. In this paper, we study the relation between the moduli spaces of modules over the sheaf of even Clifford algebras and the Prym variety associated to the conic fibration. In particular, we construct a rational map from the moduli space of modules over the sheaf of even Clifford algebras to the special subvarieties in the Prym variety, and check that the rational map is birational in some cases. As an application, we get an explicit correspondence between instanton bundles of minimal charge on cubic threefolds and twisted Higgs bundles on curves.

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arXiv2022

Semi-polarized meromorphic Hitchin and Calabi-Yau integrable systems

It was shown by Diaconescu, Donagi and Pantev that Hitchin systems of type ADE are isomorphic to certain Calabi-Yau integrable systems. In this paper, we prove an analogous result in the setting of meromorphic Hitchin systems of type A which are known to be Poisson integrable systems. We consider a symplectization of the meromorphic Hitchin integrable system, which is a semi-polarized integrable system in the sense of Kontsevich and Soibelman. On the Hitchin side, we show that the moduli space of unordered diagonally framed Higgs bundles forms an integrable system in this sense and recovers the meromorphic Hitchin system as the fiberwise compact quotient. Then we construct a new family of quasi-projective Calabi-Yau threefolds and show that its relative intermediate Jacobian fibration, as semi-polarized integrable systems, is isomorphic to the moduli space of unordered diagonally framed Higgs bundles.

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