arXiv research

Abstract: Review and properties of Gieseker stability for Higgs sheaves.

New stability criteria for vector bundles linked to Hermite-Einstein geometry.

In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to a …

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X together with a smooth divisor D such that K_X \otimes [D] is ample. It turns out tha…

New obstruction found for Hull-Strominger system solutions.

The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle satisfies the Mumford-Takemoto stability condition. In this paper we consider a…

New metrics found on non-Kähler complex manifolds.

We prove the existence of extremal, non-csc, Kähler metrics on certain unstable projectivised vector bundles $¶(E) \to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles $E \to M$ under consideration are assumed to split as a …

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact Kähler manifolds and we present some basic properties of it. In particular, we show that its gradient flow can be wr…

Equivalence proven between divisorial stability and quotient log divisorial stability.

Study on stability of harmonic maps under Ricci flow.

Introduces stability conditions for polarized varieties, linking to K-stability.

Proves criteria for uniform K-stability of log Fano pairs.

Shows uniform K-stability is open in Q-Gorenstein families of Q-Fano varieties.

Introduces valuative stability for polarised varieties, equivalent to K-stability.

The homology groups of many natural sequences of groups $\{G_n\}_{n=1}^{\infty}$ (e.g. general linear groups, mapping class groups, etc.) stabilize as $n \rightarrow \infty$. Indeed, there is a well-known machine for proving such results that goes back to early work of Quillen. Church and Farb discovered that many sequ…

We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a dynamical stability and it refers to a convergence of a Ricci flow starting at any metric in a neighbourhood of a considere…

Decomposes J-energy into simpler intersection numbers for stability analysis.

Paper discusses K-stability of pairs and its implications.

Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.

Study on stability of hyperkähler flow in 4-manifolds.

The paper introduces new metrics and stability criteria for complex manifolds.

For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in the group of all holomorphic automorphisms of $X$. Then strong relative K-stability will be shown to imply asymptotic relative Chow-stability. In particular, by taking $T$ to be trivial, we see that asymptotic Chow-stability follows from stron…

Introduces new stability concept for Fano fibrations.

This paper enhances stability selection by evaluating overall results robustness and identifying optimal regularization values.

Solves modified conjecture for Fano manifolds using Ding stability.

The paper proves stability for contact groupoids and deformations.

This work explores the trade-offs between stability and accuracy in statistical estimation.

The paper examines stability of harmonic and symphonic maps with forms and potentials.

New stability concept tested via volume function for Fano manifolds.

New stability measures for similar features improve feature selection accuracy.

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear stability of such gradient Ricci solitons.

In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.

The paper analyzes how stacking improves model stability.

Introduces relative stability conditions on triangulated categories.

Surveying Morse boundaries and stability results.

Study links K-stability of certain surfaces to binary forms, proving stability and non-stability conditions.

New stability results for configuration space cohomology.

We show that if a contact open book $(Σ,h)$ on a $(2n+1)$-manifold $M$ ($n\geq1$) is induced by a Lefschetz fibration $π:W \to D^2$, then there is a one-to-one correspondence between positive stabilizations of $(Σ,h)$ and \emph{positive stabilizations} of $π$. More precisely, any positive stabilization of $(Σ,h)$ is in…

Extends Minkowski stability proof to minimal decay assumptions.

Study strict stability of cones with isolated singularities.

Stability conditions on K3 surfaces are linked to the masses of spherical objects.

Paper relaxes stability and generalization assumptions for SGD.

The study provides criteria for K-stability of Fano varieties using anticanonical Q-divisors.

Stability of chiral rings in N=1 theories linked to K-stability of X.

New stability theorem for nonorientable surfaces mapping class groups.

The study examines the stability of Engel-like structures in higher dimensions.

The paper explores how the cohomology of certain space arrangements stabilizes as the number of subspaces increases.