Related papers: A stable version of Terao conjecture

We prove an effective restriction theorem for stable vector bundles $E$ on a smooth projective variety: $E|_D$ is (semi)stable for all irreducible divisors $D \in |kH|$ for all $k$ greater than an explicit constant. As an application, we…

We show that the locally free sheaf of locally exact differentials on a smooth projective curve of genus at least two over an algebraically closed field k of characteristic p is a stable vector bundle. This answers a question of Raynaud.

We discuss conjectures following from the attractor mechanism in type II string theory about the possible Chern classes of stable holomorphic vector bundles on Calabi-Yau threefolds. In particular, we give sufficient conditions for Chern…

We extend the concept of Segre's Invariant to vector bundles on a surface $X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle with given Chern's classes. The irreducibility of…

For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of…

We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].

We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…

We analyze the classical stability of Q-tubes --- charged extended objects in $(3+1)$-dimensional complex scalar field theory. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows…

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

Persistence diagram (PD) bundles, a generalization of vineyards, were introduced as a way to study the persistent homology of a set of filtrations parameterized by a topological space $B$. In this paper, we present an algorithm for…

In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on…

In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.

We study stable rationality of conic bundles $X$ over $\mathbb{P}^1$ defined over non-closed field $k$ via the cohomology of the Galois group of finite field extension $k'/k$ with action on the geometric Picard lattice of $X$.

We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two…

We study the orientability of vector bundles with respect to a family of cohomology theories called $\mathrm{EO}$-theories. The $\mathrm{EO}$-theories are higher height analogues of real $\mathrm{K}$-theory $\mathrm{KO}$. For each…

We determine the stability/instability of the tangent bundles of the Fano varieties in a certain class of two orbit varieties, which are classified by Pasquier in 2009. As a consequence, we show that some of these varieties admit unstable…

We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus $1$. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We…

The purpose of this paper is to clarify all of the uniformly relatively Ding stable toric Fano threefolds and fourfolds as well as unstable ones. The key player in our classification result is the Mabuchi constants, which can be calculated…

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…