Related papers: Geometric rationality of equal-rank Satake compact…

A well known conjecture asserts that a cubic fourfold X is rational if it has a cohomologically associated K3 surface. G.Ouchi proved that if X admits a finite group G of symplectic automorphisms, whose order is different from 2, then X has…

Looijenga has introduced new compactifications of locally symmetric varieties that give a complete understanding of the period map from the GIT moduli space of plane sextics to the Baily-Borel compactification of the moduli space polarized…

Let $L$ be a simply-connected simple connected algebraic group over a number field $F$, and $H$ be a semisimple absolutely maximal connected $F$-subgroup of $L$. Under a cohomological condition, we prove an asymptotic formula for the number…

We prove the geometric Satake equivalence for mixed Tate motives over the integral motivic cohomology spectrum. This refines previous versions of the geometric Satake equivalence for split reductive groups. Our new geometric results include…

We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifcations. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications.…

We study the moduli space $\mathcal{F}_{T_1}$ of quasi-trielliptic K3 surfaces of type I, whose general member is a smooth bidegree $(2,3)$-hypersurface of $\mathbb{P}^1\times \mathbb{P}^2$. Such moduli space plays an important role in the…

Let $G$ be a real semisimple Lie group with finite center and let $\mathfrak g=\mathfrak k \oplus \mathfrak p$ be a Cartan decomposition of its Lie algebra. Let $K$ be a maximal compact subgroup of $G$ with Lie algebra $\mathfrak k$ and let…

The phase space of a compact, irreducible, simply connected, Riemannian symmetric space admits a natural family of K\"ahler polarizations parametrized by the upper half plane $S$. Using this family, geometric quantization, including the…

We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We…

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special…

We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,\Gamma) where K is a Kaehler manifold and \Gamma a discrete Lie group of…

We construct the geometric Satake equivalence for quasi-split reductive groups over nonarchimedean local fields, using \'etale Artin-Tate motives with $\mathbb{Z}[\frac{1}{p}]$-coefficients. We consider local fields of both equal and mixed…

The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup $K_{g,1}$ of the mapping class group of a genus g surface with one marked point is finite-dimensional. Building on work of…

Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet $X$ and output alphabet $Y$ can be naturally endowed with the quotient of the Euclidean topology by the…

Let B be the complex n-dimensional ball and X' be the toroidal compactification of a quotient B/G by a torsion free lattice G of SU(n,1). For an arbitrary G-rational boundary point p, denote by U(p) the commutant of the unipotent radical of…

In this paper we prove a coherent version of geometric Satake equivalence proposed in Cautis-Williams' work arXiv:2306.03023 for type A. In their work, they studied an abelian version of the classical limit Satake category, namely, the…

The moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient, as a Baily--Borel compactification of a ball quotient, and as a compactified $K$-moduli space. From all three…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature.…

We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some…