arXiv subjects

Dongjian Wu

Publications and source records attributed to Dongjian Wu.

8 recordsLinked to original sources

arXiv2026

The Global Dimension Function on Stability Manifolds

In this paper, we study the reachability and boundary behavior of the global dimension function on Bridgeland stability manifolds. For a smooth projective variety $X$ of dimension $n$, we prove that the infimum of the global dimension function is $n$. This value is attained when $-K_X$ is ample, is taken by every stability condition when $K_X\in\mathrm{Pic}^0(X)$, and is not attained when $K_X$ is big and nef. We also extend these reachability results to pre-stability conditions. In addition, we construct compactifications of reduced stability spaces of smooth projective curves to which the global dimension function extends continuously. Finally, we discuss algebraic models of the reachability problem, including finite-dimensional algebras and semiorthogonal decompositions.

math.AG↗

arXiv2026

The $G$-Noncommutative Minimal Model Program

In this paper, we study the $G$-equivariant noncommutative minimal model program ($G$-NMMP), as an equivariant generalization of the framework introduced in arXiv:2301.13168. The aim of this program is to construct quasi-convergent paths in the spaces of Bridgeland stability conditions on derived categories of $G$-equivariant coherent sheaves. For finite groups, we employ induction techniques to construct such paths from the non-equivariant setting. In the setting of algebraic group actions, we introduce the notion of $\mathbb T$-stability conditions to reformulate the proposal, and then we construct quasi-convergent paths for equivariant projective spaces from small quantum cohomology.

math.AG↗

arXiv2025

Stability Conditions and Algebraic Hearts for Acyclic Quivers

We study stability conditions on the derived category of a finite connected acyclic quiver. We prove that, for any stability condition on the derived category, its heart can be obtained from an algebraic heart by a rotation of phases. Consequently, we establish the connectedness of the space of stability conditions. Furthermore, we prove that every stability condition $σ$ admits a full $σ$-exceptional collection.

math.RT↗

arXiv2025

Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras

We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs, using the geometric models and the intersection formula in \cite{QZZ}. Using the similar argument in \cite{BS, BMQS, CHQ}, we extend this identification to an isomorphism between the spaces of stability conditions and of quadratic differentials.

math.RT↗

arXiv2025

A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions

We show that the Jordan-Hölder property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition.

math.RT↗

arXiv2024

Relative Stability Conditions on Triangulated Categories

We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the deformation of gluing stability conditions in arXiv:0902.0323. The motivation for this concept stems from the discussions in arXiv:2004.04831 concerning the relationship between Bridgeland stability and the existence of the deformed Hermitian-Yang-Mills metrics on line bundles.

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arXiv2024

Stability Conditions on $\mathbb P^3$

We construct a subset of the space of stability conditions for any projective threefold with an ample polarization that satisfies a certain Bogomolov-Gieseker inequality to refine the result in arXiv:1410.1585. Then, we demonstrate that the global dimension, as defined in arXiv:2008.00282 and arXiv:1807.00469, is 3 for any stability condition on $\mathbb P^3$ constructed in arXiv:1410.1585. Finally, we formulate a conjecture concerning the contractibility of a principal connected component of $\mathrm{Stab}(\mathbb P^3)$.

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arXiv2023

Riemann-Hilbert problems from rank 3 WKB spectral networks

We extract cluster structures and establish spectral coordinates from rank 3 WKB spectral networks $\mathcal W(φ,\vartheta)$ when zeros of $φ(z)$ are almost on a line in the complex plane. Then, we provide solutions to the Riemann-Hilbert problems (cf. arXiv:1611.03697) defined by these WKB spectral networks, using the spectral coordinates. As an application, we embed spaces of framed polynomial cubic differentials, associated with these WKB spectral networks, into spaces of stability conditions, adopting the approach of arXiv:1302.7030.

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