2026-03-10
Francesco Antonio Denisi, Ángel Ortiz, Nikolaos Tsakanikas, Zhixin Xie
We introduce and study the class of primitive Enriques varieties, whose smooth members are Enriques manifolds. We provide several examples and we demonstrate that this class is stable under the operations of the Minimal Model Program (MMP). In particular, given an Enriques manifold $Y$ and an effective $\mathbb{R}$-divisor $B_Y$ on $Y$ such that the pair $(Y,B_Y)$ is log canonical, we prove that any $(K_Y + B_Y)$-MMP terminates with a minimal model $(Y',B_{Y'})$ of $(Y,B_Y)$, where $Y'$ is a $\mathbb{Q}$-factorial primitive Enriques variety with canonical singularities. Finally, we investigate the asymptotic theory of Enriques manifolds.
2026-01-26
William Sarem
Let $\Gamma$ be a discrete and torsion-free subgroup of $\PU(n,1)$, the group of biholomorphisms of the unit ball in $\C^{n}$, denoted by $\HNC$. We show that if $\Gamma$ is Abelian, then $\HNC/\Gamma$ is a Stein manifold. If the critical exponent $\delta(\Gamma)$ of $\Gamma$ is less than 2, a conjecture of Dey and Kapovich predicts that the quotient $\HNC/\Gamma$ is Stein. We confirm this conjecture in the case where $\Gamma$ is parabolic or geometrically finite. We also study the case of quotients with $\delta(\Gamma)=2$ that contain compact complex curves and confirm another conjecture of Dey and Kapovich. We finally show that $\HNC/\Gamma$ is Stein when $\Gamma$ is a parabolic or geometrically finite group preserving a totally real and totally geodesic submanifold of $\HNC$, without any hypothesis on the critical exponent.
2026-01-18
Joshua Jeishing Wen
We prove that for generic parameters, the quantum radial parts map of Varagnolo and Vasserot gives an isomorphism between the spherical double affine Hecke algebra of $GL_n$ and a quantized multiplicative quiver variety, as defined by Jordan.
2025-12-07
Paul Seidel
We introduce operations with p - adic integer coefficients, associated to idempotents in the quantum cohomology of a monotone symplectic manifold, and apply them to the structure of the quantum connection.
2025-11-01
Noemi David, Alpar R. Meszaros, Filippo Santambrogio
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials.