Related papers: A stable version of Terao conjecture

Let $G$ be a complex linear algebraic group which is simple of adjoint type. Let $\overline G$ be the wonderful compactification of $G$. We prove that the tangent bundle of $\overline G$ is stable with respect to every polarization on…

In this article we study smooth families of stratified bundles in positive characteristic and the variation of their monodromy group.Our aim is, in particular, to strengthen the weak form of the positive equicharacteristic $p$-curvature…

This paper contains results on stable bundles of rank 2 with space of sections of dimension 4 on a smooth irreducible projective algebraic curve $C$. There is a known lower bound on the degree for the existence of such bundles; the main…

We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod $p$ singular cohomology of a space, for $p$ a prime. The first extends and refines earlier work of the second and fourth…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

We formulate an effective variant of the Yau-Tian-Donaldson conjecture, then review effective results on K-stability of spherical varieties, that is, K-stability criterions which can be effectively computed given the combinatorial data…

Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of…

The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a…

Extending the work of Liu--Mubayi--Reiher~\cite{LMR23unif} on hypergraph Tur\'{a}n problems, we introduce the notion of vertex-extendability for general extremal problems on hypergraphs and develop an axiomatized framework for proving…

In this paper, we establish characterizations of variational $s$-convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic bundles, a kind of primal-dual generalized second-order…

This paper concerns the recent Virasoro conjecture for the theory of stable pairs on a 3-fold proposed by Oblomkov, Okounkov, Pandharipande and the author in arXiv:2008.12514. Here we extend the conjecture to 3-folds with…

In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…

The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…

By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

Let $Y$ be a smooth projective surface defined over an algebraically closed field $k$ with ${\rm Char}\ k\nmid n$, and let $\pi:X\rightarrow Y$ be a $n$-cyclic covering branched along a smooth divisor $B$. We show that under some conditions…

A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbb{P}^1 \times \mathbb{P}^1$…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…