Related papers: Boundedness of klt good minimal models

Let $G$ be a connected reductive group over an algebraically closed field $\Bbbk$. Under mild restrictions on the characteristic of $\Bbbk$, we show that any $G$-module with a good filtration also has a good filtration as a module for the…

Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. Applications include…

We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties.…

In this article, we propose a boundedness conjecture for the regional fundamental group of klt singularities. We prove that this boundedness conjecture, the Zariski closedness of the diminished base locus of $K_X$, and an upper bound for…

Using representations of vertex operator algebras, we describe the line bundles on a wide range of contractions of $\overline{\rm{M}}_{0,n}$, the moduli space of stable $n$-pointed rational curves, by proving a stronger version of the…

We provide bounds on the sizes of the gaps -- defined broadly -- in the set $\{k_1\beta_1 + \ldots + k_n\beta_n \mbox{ (mod 1)} : k_i \in \mathbb Z \cap (0,Q^\frac{1}{n}]\}$ for generic $\beta_1, \ldots, \beta_n \in \mathbb R^m$ and all…

Let (X,D) be a dlt pair, where X is a normal projective variety. Let S denote the support of the rounddown of D, and K the canonical divisor of X. We show that any smooth family of canonically polarized varieties over X\S is isotrivial if…

Consider a fibred compact K\"ahler manifold X endowed with a relatively ample line bundle, such that each fibre admits a constant scalar curvature K\"ahler metric and has discrete automorphism group. Assuming the base of the fibration…

The equidistribution of roots of quadratic congruences with prime moduli depends crucially upon effective bounds for a special Weyl linear form. Duke, Friedlander and Iwaniec discovered a strong estimate for this Weyl linear form when the…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, we prove a Kato square root estimate for certain coercive…

In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

We prove that the total Cartier index of a bounded family of projective varieties of klt type is bounded.

Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties. In particular this enables us to associate a Kac-Moody root system to such connections (yielding…

Hilbert curves of special varieties like Fano manifolds of low coindex as well as fibrations having such a manifold as general fiber, endowed with appropriate polarizations, are investigated. In particular, all most relevant varieties…

We show that volumes and related limits in terms of the Kodaira-Iitaka dimension exist for line bundles and graded linear series on compact reduced complex analytic spaces.

We give degree lower bounds for quotient line bundles of the lowest piece of a Hodge module induced by a complex variation of Hodge structures outside a simple normal crossing divisor, beyond the unipotent variation case. This note aims to…

In order to prove new existence results in Brill-Noether theory for rank-2 vector bundles with fixed special determinant, we develop foundational definitions and results for limit linear series of higher-rank vector bundles. These include…

We prove that rationally connected Calabi--Yau 3-folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected $3$-folds of $\epsilon$-CY type form a birationally bounded…