Related papers: Canonical Artin Stacks over Log Smooth Schemes

We introduce conjectures relating the Chow ring of a smooth Artin stack $\mathcal{X}$ to the Chow groups of its possibly singular good moduli space $X$. In particular, we conjecture the existence of an intersection product on a subgroup of…

We compactify the moduli stack of maps from curves to certain quotient stacks $\mathcal{X}=[W/G]$ with a projective good moduli space, extending previous results from quasimap theory. For doing so, we introduce a new birational…

The purpose of this paper is to lay the foundations of a theory of invariants in \'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get…

This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment…

In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a superstack as a stack over the \'etale site of superschemes, we…

We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the…

In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that…

The Chow quotient of a toric variety by a subtorus, as defined by Kapranov-Sturmfels-Zelevinsky, coarsely represents the main component of the moduli space of stable toric varieties with a map to a fixed projective toric variety, as…

We classify the Deligne-Mumford stacks M compactifying the moduli space of smooth $n$-pointed curves of genus one under the condition that the points of M represent Gorenstein curves with distinct markings. This classification uncovers new…

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well known embedding theorem of Sumihiro on quasiprojective…

This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as…

We construct a smooth algebraic stack of tuples consisting of genus two nodal curves, simple effective divisors away from the nodes, and twisted fields. It provides a desingularization of the moduli of genus two stable maps to projective…

We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

This work is devoted to the study of integral $p$-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of $p$-adic Hodge theory with the \'etale…

For a proper local embedding between two Deligne--Mumford stacks Y and X, we find, under certain mild conditions, a new (possibly non-separated) Deligne--Mumford stack X', with an etale, surjective and universally closed map to the target…

We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables…

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…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

We introduce the notion of strong regular embeddings of Deligne-Mumford stacks. These morphisms naturally arise in the related contexts of generalized Euler sequences and hypertoric geometry.