相关论文: Coherence of local and global hulls

We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A).

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border…

Let $(C,\underline{w})$ be a polarized nodal reducible curve. In this paper we consider coherent systems of type $(r,d,k)$ on $C$ with $k < r$. We prove that the moduli spaces of $(\underline{w},\alpha)$-stable coherent systems stabilize…

In this paper we provide some stability criteria for systems of linear subspaces of $V \otimes W$ and for systems of quotient coherent sheaves, using, respectively, the Hilbert-Mumford numerical criterion and moment map. Along the way, we…

A criterion for a functor between derived categories of coherent sheaves to be full and faithful is given. A semiorthogonal decomposition for the derived category of coherent sheaves on the intersection of two even dimensional quadrics is…

Let $X$ be a locally Noetherian scheme with a closed subscheme $Z$. Let $\mathcal{X}$ be the completion of $X$ at $Z$, considered as a formal scheme. We show that a coherent sheaf on $X$ is equivalently given by a coherent sheaf on…

We give a characterization of the support and cosupport conditions for a perverse sheaf in terms of the Whitney filtration.

We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and…

We develop a general framework for forcing with coherent adequate sets on $H(\lambda)$ as side conditions, where $\lambda \ge \omega_2$ is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent…

Given a graded monoid A with 1, one can construct a projective monoid scheme MProj(A) analogous to Proj(R) of a graded ring R. This paper is concerned with the study of quasicoherent sheaves (of pointed sets) on MProj(A), and we prove…

Bakker, Brunebarbe, Tsimerman showed in \cite{bakker2022minimal} that the definable structure sheaf $\mathcal{O}_{\mathbb{C}^n}$ of $\mathbb{C}^n$ is a coherent $\mathcal{O}_{\mathbb{C}^n}$-module as a sheaf on the site…

This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…

Let $C$ be a polarized nodal curve of compact type. In this paper we study coherent systems $(E,V)$ on $C$ given by a depth one sheaf $E$ having rank $r$ on each irreducible component of $C$ and a subspace $V \subset H^0(E)$ of dimension…

Coherent states for equally spaced, homogeneous waveguide arrays are defined, in the infinite, semiinfinite and finite cases, and resolutions of the identity are constructed, using different methods. In the infinite case, which corresponds…

We prove a sharp inequality relating the Castelnuovo--Mumford regularity of a coherent ideal sheaf to its log-canonical threshold.

We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial for the…

Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered $\mathcal{D}$-modules on a smooth stack $X$ and the category of $S^1$-equivariant…

We give positivity conditions on the embedding of a smooth variety which guarantee the normality of the secant variety, generalizing earlier results of the author and others. We also give classes of secant varieties satisfying the Hodge…

We show that a closed subscheme of a given locally noetherian scheme can be constructed by prescribing it germs at all points of the ambient scheme in a manner consistent with specialization of points, provided the resulting set of all…