Published in Mathematische Annalen
Harmonic amoebas are generalisations of amoebas of algebraic curves immersed in complex tori. Introduced by Krichever in 2014 , the consideration of such objects suggests to enlarge the scope of tropical geometry. In the present paper, we introduce the notion of harmonic morphisms from tropical curves to affine spaces and show how these morphisms c...
Published in Mathematische annalen
Given a locally integrable structure V over a smooth manifold Ω and given p ∈ Ω we define the Borel map of V at p as the map which assigns to the germ of a smooth solution of V at p its formal Taylor power series at p. In this work we continue the study initiated in Barostichi et al. (Math. Nachr. 286(14-15):1439-1451, 2013), Della Sala and Lamel (...
We give a constructive, computer-assisted proof that $\operatorname{Aut}(\mathbb{F}_5)$, the automorphism group of the free group on $5$ generators, has Kazhdan's property $(T)$.
Published in Mathematische Annalen
A similarity structure on a connected manifold M is a Riemannian metric on its universal cover M~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde{M}}$$\end{docum...
Published in Mathematische Annalen
Given a family of polynomial-like maps of large topological degree, we relate the presence of Misiurewicz parameters to a growth condition for the volume of the iterates of the critical set. This generalizes to higher dimensions the well-known equivalence between stability and normality of the critical orbits in dimension one. We also introduce a n...
Published in Mathematische Annalen
We first prove an isomorphism between the moduli space of smooth cubic threefolds and the moduli space of hyperkähler fourfolds of K3[2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...
Published in Mathematische Annalen
An algebraic variety is called A1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {A}^{1}$$\end{document}-cylindrical if it contains an A1\documentclass[12pt]{mi...
Published in Mathematische Annalen
We prove that any proper, geodesic metric space whose Dehn function grows asymptotically like the Euclidean one has asymptotic cones which are non-positively curved in the sense of Alexandrov, thus are CAT(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepac...
Published in Mathematische Annalen
A Nikulin configuration is the data of 16 disjoint smooth rational curves on a K3 surface. According to a well known result of Nikulin, if a K3 surface contains a Nikulin configuration C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepac...
Published in Mathematische Annalen
We show that a K -approximate subgroup A of a residually nilpotent group G is contained in boundedly many cosets of a finite-by-nilpotent subgroup, the nilpotent factor of which is of bounded step. Combined with an earlier result of the author, this implies that A is contained in boundedly many translates of a coset nilprogression of bounded rank a...
