Related papers: Compact moduli of hyperplane arrangements

We give lower bounds for the rank of the first homology group of the real points of the Deligne-Mumford-Knudsen compactification of stable n-pointed curves of genus 0,which coincides with the Chow quotient (RP^1)^n//PGL(2,R).The study has…

We extend the definition of an m-stable curve introduced by Smyth to the setting of maps to a projective variety X, generalizing the definition of a Kontsevich stable map in genus one. We prove that the moduli problem of n-pointed m-stable…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

We define two equivalent notions of twisted stable map from a curve to a Deligne-Mumford stack with projective moduli space, and we prove that twisted stable maps of fixed degree form a complete Deligne-Mumford stack with projective moduli…

We analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian--Oprea--Pandharipande moduli space of stable quotients. We…

In this paper we present a classification of possible dynamics of closed string moduli within specific toroidal compactifications of Type II string theories due to the NS-NS tadpole terms in the reduced action. They appear as potential…

We compute the rank of the first homology group and we study the higher Betti numbers of the real points of the Deligne-Mumford-Knudsen compactification of stable n-pointed curves of genus 0,which coincides with the Chow quotient…

Recent work on the log minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable…

We study compactifications of the moduli space of a plane cubic curve marked by \(n\) labeled points up to projective equivalence via Geometric Invariant Theory (GIT). Specifically, we provide a complete description of the GIT walls and…

We develop a framework to construct moduli spaces of $\mathbb{Q}$-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of $\mathbb{Q}$-stable pair. We show that these choices give a proper moduli…

We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterize when the tropical compactification of the moduli space agrees with the theory of geometric tropicalization. The…

We give a summary of joint work with Michael Thaddeus that realizes toroidal compactifcations of split reductive groups as moduli spaces of framed bundles on chains of rational curves. We include an extension of this work that covers Artin…

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective…

We show that the moduli spaces of stable sheaves on projective schemes admit certain non-commutative structures, which we call quasi NC structures, generalizing Kapranov's NC structures. The completion of our quasi NC structure at a closed…

The main result of this article is that the component of the Alexeev-Koll\'{a}r-Shepherd-Barron moduli space of stable surfaces parameterizing stable degenerations of symmetric squares of curves is isomorphic to the moduli space of stable…

We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One…

We identify the stable surfaces around the stable limit of the examples of Y. Lee and J. Park [LP07], and H. Park, J. Park and D. Shin [PPS09] using the explicit 3-fold Mori theory in [HTU13]. These surfaces belong to the…

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…

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…

This is the third paper in a series, following [FPVa] and [FPVb]. We classify all modular compactifications of the universal Jacobian over $\overline{\mathcal{M}}_{g,n}$, both as stacks and as their relative good moduli spaces. Our main…