Related papers: Toroidal compactifications and Borel--Serre compac…
We present a bijection for toroidal maps that are essentially $3$-connected ($3$-connected in the periodic planar representation). Our construction actually proceeds on certain closely related bipartite toroidal maps with all faces of…
We describe a geometric, stable pair compactification of the moduli space of Enriques surfaces with a numerical polarization of degree 2, and identify it with a semitoroidal compactification of the period space.
We give a characteristic free proof of the main result of our previous paper (math.AC/0509697) concerning toroidalization of generating sequences of valuations in dimension two function fields. We show that when an extension of two…
By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our…
We describe two geometrically meaningful compactifications of the moduli space of elliptic K3 surfaces via stable slc pairs, for two different choices of a polarizing divisor, and show that their normalizations are two different toroidal…
We compute the low degree $\ell$-adic intersection cohomology of symplectic local systems on the Satake compactification of the moduli space $A_g$ of principally polarized abelian varieties. We prove that only a small finite list of…
We introduce the tropicalization of closed subschemes of a torus defined over a higher dimensional local field. We study the basic invariants of such tropicalizations. This is a generalization of the results of Einslieder, Kapranov, Lind,…
We consider the future causal boundary as a tool to find obstructions to conformal extensions, the latter being a slight generalization to conformal compactifications.
Given a hypersurface in a complex projective space, we prove that the multidegrees of its toric polar map agree, up to sign, with the coefficients of the Chern-Schwartz-MacPherson class of a distinguished open set, namely the complement of…
Let $G$ be a connected reductive group over a $p$-adic local field $F$. R\'emy-Thuillier-Werner constructed embeddings of the (reduced) Bruhat-Tits building $\mathcal{B}(G,F)$ into the Berkovich spaces associated to suitable flag varieties…
We study the concordance and bordism of decompositions associated with defining sequences and we relate them to some invariants of toroidal decompositions and to the cobordism of homology manifolds. These decompositions are often wild…
A detailed study of the charge spectrum of three dimensional Abelian Topological Massive Gauge Theory (TMGT) is given. When this theory is defined on a manifold with two disconnected boundaries there are induced chiral Conformal Field…
The divisors on $\bar{\operatorname{M}}_g$ that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of $\operatorname{A}_g$ form a 2-dimensional extremal face of the nef cone of…
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of…
In this paper we focus on compacta $K \subseteq \mathbb{R}^3$ which possess a neighbourhood basis that consists of nested solid tori $T_i$. We call these sets toroidal. In \cite{hecyo1} we defined the genus of a toroidal set as a…
Inspired by the ideas of the minimal model program, Shepherd-Barron, Koll\'ar, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest…
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these…
We continue our study of the geometry of Nieto's quintic threefold, looking at degenerate surfaces that correspond to certain loci and showing how they arise from a toroidal compactification of a suitable moduli space.
In this note we prove the Borel Conjecture for closed, irreducible and sufficiently collapsed three-dimensional Alexandrov spaces. We also pose several questions related to characterization of fundamental groups of three-dimensional…
Periodenbereiche sind gewisse offene Unterraeume von verallgemeinerten Flaggenvarietaeten, welche durch Semistabilitaetsbedingungen beschrieben werden. In dem Fall eines endlichen Grundkoerpers bilden diese eine Zariski-offene…