相关论文: A Compactification of the Space of Plane Curves
We construct a compactification M_d of the moduli space of plane curves of degree d. We regard a plane curve C as a surface-divisor pair (P^2,C) and define M_d as a moduli space of pairs (X,D) where X is a degeneration of the plane. We show…
Consider the moduli space M^0 of arrangements of n hyperplanes in general position in projective (r-1)-space. When r=2 the space has a compactification given by the moduli space of stable curves of genus 0 with n marked points. In higher…
The minimal model program suggests a compactification of the moduli space of hyperplane arrangements which is a moduli space of stable pairs. Here, a stable pair consists of a scheme X which is a degeneration of projective space and a…
The goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ surfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in…
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…
The space of smooth rational curves of degree $d$ in a projective variety $X$ has compactifications by taking closures in the Hilbert scheme, the moduli space of stable sheaves or the moduli space of stable maps respectively. In this paper…
The moduli spaces of stable surfaces serve as compactifications of the moduli spaces of canonical models of smooth surfaces in the same way the moduli spaces of stable curves compactify the moduli spaces of smooth curves. However, the…
We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objects, as opposed to line bundles on stacky curves. For all m,…
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 give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divisor by Alexeev. The construction is an application…
We construct a good compactification of the variety of irreducible projective plane curves of degree n with d nodes and no other singularities.
In this paper, we study all ways of constructing modular compactifications of the moduli space $\mathcal{M}_{g,n}$ of $n$-pointed smooth algebraic curves of genus $g$ by allowing markings to collide. We find that for any such…
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 explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2. The space parametrizes log pairs $(S, D)$ where $S$ is a degeneration of $\mathbb{P}^1 \times \mathbb{P}^1$ and $D \subset S$ is a…
Projective duality identifies the moduli spaces $\mathbf{B}_n$ and $\mathbf{X}(3,n)$ parametrizing linearly general configurations of $n$ points in $\mathbb{P}^2$ and $n$ lines in the dual $\mathbb{P}^2$, respectively. The space…
The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the…
Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P^1 of degree d totally ramified over the two marked points, for d>= 2. Such loci have codimension two. We compute the class…
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 consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical…
We construct several modular compactifications of the Hurwitz space $H^d_{g/h}$ of genus $g$ curves expressed as $d$-sheeted, simply branched covers of genus $h$ curves. These compactifications are obtained by allowing the branch points of…