arXiv subjects

Nantao Zhang

Publications and source records attributed to Nantao Zhang.

4 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 on blowups

We study the relation between perverse stability conditions and geometric stability conditions under blow up. We confirm a conjecture of Toda in some special cases and show that geometric stability conditions can be induced from perverse stability conditions from semiorthogonal decompositions associated to blowups.

math.AG↗

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 $\mathrm{Stab}(\mathbb P^3)$.

math.AG↗