Related papers: Semipositivity theorems for moduli problems

We prove that if a quasi-tilted algebra is tame, then the associated moduli spaces are products of projective spaces. Together with an earlier result of Chindris this gives a geometric characterization of the tame quasi-tilted algebras.

We study cohomology support loci of regular holonomic D-modules on complex abelian varieties, and obtain conditions under which each irreducible component of such a locus contains a torsion point. One case is that both the D-module and the…

This is a sequel to "Kodaira-Saito vanishing via Higgs bundles in positive characteristic" (arXiv:1611.09880). However, unlike the previous paper, all the arguments here are in characteristic zero. The main result is a Kodaira vanishing…

We further develop the general theory of the "mixed modular derived category" introduced by the authors in a previous paper in this series. We then use it to study positivity and Q-Koszulity phenomena on flag varieties.

This paper solves the global moduli problem for regular holonomic D-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to…

We find some equivalences of the derived category of coherent sheaves on a Gorenstein genus one curve that preserve the (semi)-stability of pure dimensional sheaves. Using them we establish new identifications between certain Simpson moduli…

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 develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles…

We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an…

We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual…

A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these…

Let $\textbf{H} = ((H, F^{\bullet}), L)$ be a polarized variation of Hodge structure on a smooth quasi-projective variety $U.$ By M. Saito's theory of mixed Hodge modules, the variation of Hodge structure $\textbf{H}$ can be viewed as a…

We construct a quasi-categorically enhanced Grothendieck six-functor formalism on schemes of finite type over the complex numbers. In addition to satisfying many of the same properties as M. Saito's derived categories of mixed Hodge…

We study a variant of the semi-stable Cohomological Hall algebra which we construct using equivariant Chow groups. This algebra, we call it the semi-stable ChowHa, arises as a quotient of the CoHa. Smooth models of quiver moduli give rise…

Let SU_X(n,L) be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g>1 curve X. Let SU_X^s(n,L) denote the open subset parameterizing stable bundles. We show that for small i, the…

A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.

We prove that a variation of graded-polarizable mixed Hodge structure over a punctured disk with unipotent monodromy, has a limiting mixed Hodge structure at the puncture (i.e., it is admissible in the sense of [SZ]) which splits over $\R$,…

Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructible families of finely graded modules over constructible…

In this note we define moduli functors of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the…