Related papers: The WYSIWYG compactification
We provide a new construction of Huber's universal compactification in the case of the structure morphism of a quasi-compact, separated rigid analytic space over a non-archimedean field. We make use of Raynaud's theory of formal models and…
Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature…
We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on $CP^2$ and contracting the strict transform of a given line and all but…
We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…
We construct an explicit compactification for the space of parametrized rational curves in a Grassmanian by a nonsingular projective variety such that the boundary is a divisor with simple normal crossings. This compactification is obtained…
The main purpose of this paper is to present a conceptual approach to understanding the extension of the Prym map from the space of admissible double covers of stable curves to different toroidal compactifications of the moduli space of…
In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described…
We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the…
All arithmetic non-compact ball quotients by Deligne-Mostow's unitary monodromy group arise as sub-ball quotients of either of two spaces called ancestral cases, corresponding to Gaussian or Eisenstein Hermitian forms respectively. In a…
We extend the Global Compactness result by M. Struwe (Math. Z, 1984) to any fractional Sobolev spaces $\dot{H}^s(\Omega)$ for $0<s<N/2$ and $\Omega \subset \mathbb{R}^N$ a bounded domain with smooth boundary. The proof is a simple direct…
We prove the following result: Let B be a smooth, irreducible, quasi-projective variety over the complex numbers and assume that B has a projective compactification \bar{B} such that \bar{B} - B is of codimension at least two in \bar{B}.…
We introduce the partial reductions and inverse Hamiltonian reductions between affine $\mathcal{W}$-algebras along the closure relations of associated nilpotent orbits in the case of $\mathfrak{sl}_4$, fulfilling all the missing…
Let $G$ be a connected semi-simple algebraic group of adjoint type over an algebraically closed field, and let $\overline{G}$ be the wonderful compactification of $G$. For a fixed pair $(B, B^-)$ of opposite Borel subgroups of $G$, we look…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
The purpose of this paper is to describe an analogue of a construction of Costello in the context of finite-dimensional differential graded Frobenius algebras which produces closed forms on the decorated moduli space of Riemann surfaces. We…
We describe the GIT compactification of the moduli of (2,2)-type effective divisors of $\mathbb{P}^1\times\mathbb{P}^2$ (i.e., surfaces of the linear system $\vert \pi_1^*\mathcal{O}_{\mathbb{P}^1}(2)\otimes…
This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for…
In the seminal paper of Borel and Tits about reductive groups, they show some fundamental results about Bruhat cells with respect to a minimal parabolic subgroup, e.g., relative Bruhat decomposition and its geometrization, relative Bruhat…
We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $\mathcal{A}_{q,p}\big(\widehat{\mathfrak{gl}}(N)_{c}\big)$. We identify two sets of conditions…
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…