Related papers: Stability of Kernel Sheaves on Del Pezzo Surfaces
We describe the GIT compactification of the moduli of (2,2)-type effective divisors of $\mathbb{P}^1\times\mathbb{P}^2$ (i.e., surfaces of the linear system $\vert \pi_1^*\mathcal{O}_{\mathbb{P}^1}(2)\otimes…
In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a…
The spectral side of the (conjectural) Betti geometric Langlands correspondence concerns sheaves on the character stack of an algebraic curve; in particular, the categories in question are manifestly invariant under deformations of the…
We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent…
We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric…
In previous works, the authors investigated the relationships between linear stability of a generated linear series $|V|$ on a curve $C$, and slope stabillity of the vector bundle $M_{V,L} := \ker (V \otimes \mathcal{O}_C \to L)$. In…
We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the…
On a normal projective variety the locus of $\mu$-stable bundles that remain $\mu$-stable on all Galois covers prime to the characteristic is open in the moduli space of Gieseker semi-stable sheaves. On a smooth projective curve of genus at…
We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide new obstructions…
In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.
We use wall-crossing in the Bridgeland stability manifold to systematically study the birational geometry of the moduli space $M_\sigma(\mathbf{v})$ of $\sigma$-semistable objects of class $\mathbf{v}$ for a generic stability condition…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
We provide an optimal Gevrey stability result for general boundary layer expansions, under a mild concavity condition on the boundary layer profile. Our result generalizes (and even improves in the non strictly concave case) the one…
We consider the shear flow of well-aligned one-component smectic phases, such as thermotropic smectics and lamellar diblock copolymers, below the critical region. We show that, as a result of thermal fluctuations of the layers, parallel…
For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, called the Cox ring. We show that in characteristic 0 this ring…
We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
We study sextic del Pezzo surface fibrations via root stacks.
In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its…