相关论文: Strebel Differentials and stable Matrix Factorizat…

A dimer model is a bipartite graph described on the real two-torus, and it gives the quiver as the dual graph. It is known that for any three-dimensional Gorenstein toric singularity, there exists a dimer model such that a GIT quotient…

We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this…

Few changes. We compute the Hilbert series of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials.

Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the associated bounded derived categories of coherent sheaves. Assume the existence of a triangulated category T which is admissible both in D^b(X) as in D^b(Y).…

We propose a logarithmic enhancement of the Gromov-Witten/Donaldson-Thomas correspondence, with descendants, and study its behavior under simple normal crossings degenerations. The formulation of the logarithmic correspondence requires a…

For F an algebraic extension of Q2, the conjugacy classes of invertible, 2-by-2, trace-zero matrices under the action of G := SL2(F) are analyzed relative to the quadratic extension that splits the respective characteristic polynomial. The…

In the first part of our paper, we show that there exist non-isomorphic derived equivalent genus $1$ curves, and correspondingly there exist non-isomorphic moduli spaces of stable vector bundles on genus $1$ curves in general. Neither…

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic terms. Then,…

We study the relationship between two stratifications on parameter spaces for coherent sheaves and for quiver representations: a stratification by Harder-Narasimhan types and a stratification arising from the geometric invariant theory…

On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime…

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…

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…

We propose a specific class of matrices which participate in factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang-Baxter maps, expressed in non-commutative variables.…

The Stable Reduction Theorem guarantees that any smooth, projective, geometrically irreducible curve of genus $g \geq 2$ over a discretely valued field admits a unique stable model after a finite field extension. Computing this model is a…

Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order…

From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…

An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to…

We show that the existence of locally finite stability conditions on the bounded derived category $\mathbf{D}^{b}(X)$ of coherent sheaves on an affine Noetherian scheme $X$ is equivalent to $\dim X=0$. We also study the spaces of stability…

We compare the so-called clock condition to the gradability of certain differential modules over quadratic monomial algebras. For a stably hereditary algebra or a gentle one-cycle algebra, these considerations show that the orbit category…

In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…