Related papers: Moduli spaces of quantum toric stacks and their co…

Let $G$ be a reductive algebraic group. A toric principal $G$-bundle is a principal $G$-bundle over a toric variety together with a torus action commuting with the $G$-action. Extending the Klyachko classification of toric vector bundles,…

The classical Losev-Manin space is a toric compactification of the moduli space of $n$ points in the affine line modulo translation and scaling. Motivated by this, we study its higher-dimensional toric counterparts, which compactify the…

Gallardo and Routis constructed compactifications of the moduli space of $n$ labeled points in $\mathbb{P}^d$ by assigning weights to points, generalizing Hassett's weighted compactifications of $M_{0,n}$ to higher-dimensional projective…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

The space of smooth curves admits a beautiful compactification by the moduli space of Deligne-Mumford stable curves. In this paper, we undertake a systematic investigation of alternate modular compactifications of the space of smooth…

We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi--projective. This contradicts a recent paper…

We define a natural compactification of an arrangement complement in a ball quotient. We show that when this complement has a moduli space interpretation, then this compactification is often one that appears naturally by means of geometric…

We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as…

We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…

We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper…

We contribute to the foundations of tropical geometry with a view towards formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show…

For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T^1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y…

The logarithmic multiplicative group is a proper group object in logarithmic schemes, which morally compactifies the usual multiplicative group. We study the structure of the stacks of logarithmic maps from rational curves to this…

We study the compactification of the moduli space of a certain class of rank-two irregular connections on the Riemann sphere, presenting one double pole and two simple poles. To construct the compactification explicitly, we identify a class…

We study a compactification of the moduli space of theta characteristics, giving a modular interpretation of the geometric points and describing the boundary stratification. This space is different from the moduli space of spin curves. The…

We call complex quasifold of dimension k a space that is locally isomorphic to the quotient of an open subset of the space C^k by the holomorphic action of a discrete group; the analogue of a complex torus in this setting is called a…

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this…

We describe a framework to construct tropical moduli spaces of rational stable maps to a smooth tropical hypersurface or curve. These moduli spaces will be tropical cycles of the expected dimension, corresponding to virtual fundamental…

We study the moduli space of A/2 half-twisted gauged linear sigma models for NEF Fano toric varieties. Focusing on toric deformations of the tangent bundle, we describe the vacuum structure of many (0,2) theories, in particular identifying…

In this note we introduce a new family of non-commutative spaces that we call non-commutative toric varieties and we describe some of their main properties. The main technical tool in this investigation is a natural extension of LVM-theory…