Related papers: Semiample invertible sheaves with semipositive con…

Let S be an algebraic space, A an S-abelian algebraic space, L an S-fiberwise numerically trivial invertible module on A, and L* the sheaf of regular sections of L considered as a G_m-torsor on A. We classify the S-minimal models of L* into…

For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L, \phi)$ over it, we establish a metric extension result for sections of $L^{\otimes n}$ from a…

We introduce $\hat{H}$-eigenvalue for $2m$-th order $n$-dimensional complex tensors. Then we determine several checkable inclusion sets for $\hat{H}$-eigenvalues and derive some criterions for the Hermitian positive definiteness…

Let $(X, H)$ be a normal complex projective polarized variety and $\mathscr E$ an $H$-semistable sheaf on $X$. We prove that the restriction $\mathscr E\big|_C$ to a sufficiently positive general complete intersection curve $C \subset X$…

In this article, we prove a semi-continuity property for both conductor divisors and logarithmic conductor divisors for \'etale sheaves on higher relative dimensions in a geometric situation. It generalizes a semi-continuity result for…

In this paper we construct a tilting sheaf for Severi-Brauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

Let \(E\) be a finite-dimensional real vector space. We study invertible objects in the monoidal category of constructible sheaves on \(E\), endowed with the convolution product \(\star\). We show that the inverse of an invertible…

Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider framed sheaves on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent…

On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with…

We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus $T$ as an ind-object in the category of holomorphic vector bundles on $T$. Extending the results of math.QA/0211262 and math.QA/0308136 we prove that the…

We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…

A quasi-isometry between two connected graphs is measure-scaling if one can control precisely the sizes of pre-images of finite subsets. Such a notion is motivated by the work of Eskin-Fisher-Whyte on lamplighters over $\mathbb{Z}$ and the…

As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds.…

We show that pure strongly continuous semigroups of adjointable isometries on a Hilbert C*-module are standard right shifts. By counter examples, we illustrate that the analogy of this result with the classical result on Hilbert spaces by…

Using methods of stable homotopy theory, the category of symmetric quasi-coherent sheaves associated with non-commutative graded algebras with extra symmetries is introduced and studied in this paper. It is shown to be a closed symmetric…

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer…

Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…

In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal character sheaves. This constitutes a major step towards the…

The aim of this paper is to show that two accessible subspaces in the Loynes $\mathcal{Z}$ - space $\Hc$ are the initial and final space of a partial gramian isometry, respectively if the norm of the difference of the associated gramian…