Related papers: Stable automorphic forms for the general linear gr…
We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…
In this paper, we prove modularity results of Taylor coefficients of certain non-holomorphic Jacobi forms. It is well-known that Taylor coefficients of holomorphic Jacobi forms are quasimoular forms. However recently there has been a wide…
Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…
The systematic study of harmonic self-maps on cohomogeneity one manifolds has recently been initiated by P\"uttmann and the second named author in \cite{MR4000241}. In this article we investigate the corresponding Jacobi equation describing…
In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
In the present paper, we study a new kind of anabelian phenomenon concerning the smooth pointed stable curves in positive characteristic. It shows that the topological structures of moduli spaces of curves can be understood from the…
We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised tori, such as $L$-groups of (possibly non-split) tori. We show that the corresponding deformation rings are formally smooth over a…
Recently, a classical approach to continuous structures has been proposed in [ABBMZ] and [Z] that extends the class of structures falling under the scope of [HI] or [BBHU]. These articles introduce the notion of structures with a standard…
We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear…
We introduce the notion of stable orbifold projective curves, and show that the moduli stack of stable orbifold projective curves is isomorphic to the moduli stack of weighted pointed stable curves in the sense of Hassett with respect to…
We prove that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves.
We consider principal bundles as generalized morphisms between topological groupoids. In the category of these generalized morphisms two topological groupoids are isomorphic if and only if they are Morita equivalent. We show that the fibers…
In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…
The super upper half plane, this is the ordinary upper half plane with additional odd (anticommuting) directions, admits a transitive super action of a certain super Lie group G . First we define the spaces of super automorphic and cusp…
We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…
We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of…
We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping…
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…