Related papers: Some remarks on the semi-positivity theorems

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on…

We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family of varieties parametrized by a regular complex base scheme, extending the analogous…

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is…

Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…

We consider twisted standard filtrations of Soergel bimodules associated to arbitrary Coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the Hecke algebra. This…

The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family…

We first develop a general theory of Johnson filtrations and Johnson homomorphisms for a group $G$ acting on another group $K$ equipped with a filtration indexed by a "good" ordered commutative monoid. Then, specializing it to the case…

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This…

Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two conjectures due to Kashiwara and Schapira concerning the existence of stratifications of…

We study Seiberg duality of quiver gauge theories associated to the complex cone over the second del Pezzo surface. Homomorphisms in the path algebra of the quivers in each of these cases satisfy relations which follow from a superpotential…

We give an elementary construction of homology of sheaves from Brown representability for the dual and see how its main properties are derived easily from the construction. Comparison with Poincar\'e-Verdier duality and with homology of…

Given an n-dimensional variety Z with rational singularities, we conjecture that for a resolution of singularities whose reduced exceptional divisor E has simple normal crossings, the (n-1)-th higher direct image of the sheaf of…

We formulate Vojta's conjecture for smooth weighted projective varieties, weighted multiplier ideal sheaves, and weighted log pairs and prove that all three versions of the conjecture are equivalent. In the process, we introduce generalized…

We give a new proof of Koll\'ar's conjecture on the pushforward of the dualizing sheaf twisted by a variation of Hodge structure. This conjecture was settled by M. Saito via mixed Hodge modules and has applications in the investigation of…

We identify limit stable pairs and stable framed sheaves as epimorphisms and monomorphisms, respectively, in tilts of the standard heart, under suitable conditions. We then identify the moduli spaces with the corresponding Quot spaces,…

Let $f:X\to Y$ be a morphism of complex manifolds. Suppose that $X$ is a K\"ahler manifold. Let $(\mathcal{T},\mathcal{S})$ be a regular polarized pure twistor $\mathcal{D}$-module of weight $w$ on $X$ whose support is proper over $Y$. We…

In this short note we show that the homotopy category of smooth compactifications of smooth algebraic varieties is equivalent to the homotopy category of smooth varieties over a field of characteristic zero. As an application we show that…

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure.…

We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic…