Related papers: On moduli of foliated surfaces

The notion of $m/\Gamma$-pointed stable curves is introduced. It should be viewed as a generalization of the notion of m-pointed stable curves of a given genus, where the labels of the marked points are only determined up to the action of a…

We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to…

We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…

Stable quotient spaces provide an alternative to stable maps for compactifying spaces of maps. When the target is projective space and the domain curve has genus 1, these are smooth proper Deligne-Mumford stacks. In this paper we study the…

We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is naturally identified with the moduli space of extended tropical curves, and that this is compatible with the "naive" set-theoretic tropicalization…

We define a Deligne-Mumford stack X_{D,r} which depends on a scheme X, an effective Cartier divisor D\subset X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into X_{D,r} provides…

The purpose of these notes is to give an introduction to Deligne-Mumford stacks and their moduli spaces, with emphasis on the moduli problem for curves. The paper has 4 sections. In section 1 we discuss the general problem of constructing a…

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme…

The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle.

The Deligne-Mumford stable reduction theorem asserts that for a family of stable curves over the punctured disk, after a finite base change, the family can be completed in a unique way to a family of stable curves over the disk. In this…

We propose an alternative definition for families of stable pairs $(X,D)$ over a possibly non-reduced base when $D$ is reduced, by replacing $(X,D)$ with an appropriate orbifold pair $(\mathcal X,\mathcal D)$. This definition of a stable…

We use the theory of twisted stable maps to Deligne-Mumford stacks to construct compactifications of the moduli space of pairs $(X \to C, S + F)$ where $X \to C$ is a fibered surface, $S$ is a sum of sections, $F$ is a sum of marked fibers,…

We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.

We define a proper moduli stack for degree $p$ covers $f:Y \to \cX$ where $\cX$ is a twisted stable curve in the sense of [5] and [4], and $Y$ is a stable curve which via $f$ is a torsor over $\cX$ under a finite flat group scheme $\cG \to…

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…

We construct a presentation for the Grothendieck group of Deligne-Mumford stacks over a field of characteristic zero. The generators for this presentation are smooth, proper Deligne-Mumford stacks and the relations are expressed in terms of…

We prove a representation stability result for the sequence of spaces $\overline M_{g, n}^A$ of pointed admissible $A$-covers of stable $n$-pointed genus-$g$ curves, for an abelian group $A$. For fixed genus $g$ and homology degree $i$, we…

Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…