相关论文: Low dimensional models of the finite split Cayley …

Let ${\mathcal G}_k(V)$ be the $k$-Grassmannian of a vector space $V$ with $\dim V=n$. Given a hyperplane $H$ of ${\mathcal G}_k(V)$, we define in [I. Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating $k$-linear forms, J.…

We use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces $X\subset \mathbb{P}^{n+1}$ of degree $d\leq n+1$. As an application, we compute the…

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group.…

Let $K$ be a complete discretely valued field whose residue field has characteristic different from $2$. Let $(D,\sigma)$ be a $K-$division algebra with involution of the first kind, and $h$ be a $K-$anisotropic $\epsilon$-hermitian form…

Constructions of regular heptagon and triskaidecagon by trisection of an angle are well known. An elegant construction of the heptagon by S. Adlaj shows a 3-fold symmetry related to a Galois group. Based on the latter construction, in this…

We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$.…

The kth finite subset space of a topological space X is the space exp_k X of non-empty finite subsets of X of size at most k, topologised as a quotient of X^k. The construction is a homotopy functor and may be regarded as a union of…

Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely…

We give an explicit construction of two $2$-generated subgroups $H,K\leq \SL(3,\Z)$ whose intersection is not finitely generated. The construction takes place inside the standard parabolic subgroup $\Z^2\rtimes \SL(2,\Z)\leq \SL(3,\Z)$. The…

For a fixed compact Riemann surface X, of genus at least 2, we count the number of connected components of the moduli space of maximal Higgs bundles over X for the hermitian groups $PSp(2n,R)$, $PSO^*(2n)$, $PSO_0(2,n)$ and $E_6^{-14}$.…

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

In this paper we characterize the non-singular Hermitian variety ${\mathcal H}(6,q^2)$ of $\mathrm{PG}(6, q^2)$, $q\neq2$ among the irreducible hypersurfaces of degree $q+1$ in $\mathrm{PG}(6, q^2)$ not containing solids by the number of…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

We construct a bi-Hamiltonian structure for the holomorphic spin Sutherland hierarchy based on collective spin variables. The construction relies on Poisson reduction of a bi-Hamiltonian structure on the holomorphic cotangent bundle of…

We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the…

Let $E$ be a two-dimensional \'etale algebra over a non-Archimedean local field $K$ of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over $E$ is generated by symmetries and rescaled Eichler…

The aim of this article is twofold: firstly, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual \tch-de Rham construction; secondly,…

Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are determined and their types are characterized in terms of the shape operator and the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084} and…

We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives a new geometric point of view on these…

In this paper, using the technical tools in \cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the K\"ahler case results in \cite{HMW} and \cite{DK}.