arXiv subjects

Chunhui Wei

Publications and source records attributed to Chunhui Wei.

6 recordsLinked to original sources

arXiv2026

Reduced Solutions of Toda Systems for Arbitrary Complex Simple Lie Algebras

We study reduced solutions of Toda systems generated by spherical metrics for an arbitrary complex simple Lie algebra. The main result is an intrinsic centralizer parametrization: for a spherical metric, the reduced family is the positive Iwasawa slice cut out by the centralizer of the principal image of closure of monodromy group. As an application, we transfer existing spherical-metric existence results to the diagonal Toda source tuple.

math-ph↗

arXiv2026

ALH Gravitational Instantons and Rational Surfaces

We construct complete ALH hyperkähler metrics on complements of anticanonical elliptic curves with zero self-intersection in smooth rational surfaces. This answers the existence question of Filip--Tosatti, related to the picture proposed by Haskins--Hein--Nordström. Conversely, we prove that every hyperkähler ALH gravitational instanton admits, for each induced complex structure, a compactification by an anticanonical elliptic curve in a rational surface.

math.DG↗

arXiv2026

Dévissage for Algebraic K-theory of Small Stable $\infty$-categories

In this article, we extend the theorem of heart\cite{Barwick_2015}, which implies Quillen's dévissage theorem by \cite{Efimov2025}, to generic small stable $\infty$-categories. To be precise, we establish a necessary and sufficient condition under when an exact functor between stable $\infty$-categories induces isomorphisms of non-negative $K$-groups when this exact functor satisfies the dévissage condition.

math.KT↗

arXiv2026

Noncommutative Quillen-Lichtenbaum Conjecture

We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we generalizes the conjecture through the lens of noncommutative geometry.

math.AG↗

arXiv2025

Solution to SU(n+1) Toda system generated by spherical metrics

Using the correspondence between solutions to the SU(n+1) Toda system on a Riemann surface and totally unramified unitary curves, we show that a spherical metric $ω$ generates a family of solutions, including $(i(n+1-i)ω)_{i=1}^n$. Moreover, we characterize this family in terms of the monodromy group of the spherical metric. As a consequence, we obtain a new solution class to the SU(n+1) Toda system with cone singularities on compact Riemann surfaces, complementing the existence results of Lin-Yang-Zhong (JDG, 114(2):337-391, 2020).

math-ph↗

arXiv2022

Solutions of the ${\rm SU}(n+1)$ Toda system from meromorphic functions

We consider the ${\rm SU}(n+1)$ Toda system on a simply connected domain $Ω$ in ${\Bbb C}$, the $n=1$ case of which coincides with the Liouville equation $Δu+8e^u=0$. A classical result by Liouville says that a solution of this equation on $Ω$ can be represented by some non-degenerate meromorphic function on $Ω$. We construct a family of solutions parameterized by ${\rm PSL}(n+1,\,{\Bbb C})/{\rm PSU}(n+1)$ for the ${\rm SU}(n+1)$ Toda system from such a meromorphic function on $Ω$, which generalizes the result of Liouville. As an application, we find a new class of solvable ${\rm SU}(n+1)$ Toda systems with singular sources via cone spherical metrics on compact Riemann surfaces.

math-ph↗