Related papers: Picard Groups of Stacky Curves

In this article, we study the behavior of the stability of pullback of a vector bundle under a finite morphism from a (not necessarily smooth) stacky curve to an orbifold curve. We establish a categorical equivalence between proper formal…

We use Harer's stability theorem to give another proof of his fundamental theorem: The rank of the Picard group of the moduli space of smooth projective curves of genus g > 2 equals one.

We define stacks of uniform cyclic covers of Brauer-Severi schemes, proving that they can be realized as quotient stacks of open subsets of representations, and compute the Picard group for the open substacks parametrizing smooth uniform…

We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first…

We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of the affine line to be non trivial…

We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index

We show that for any stable sheaf $E$ of slope $> 2g-1$ on a smooth, projective curve of genus $g$, the associated Picard sheaf $\hat{E}$ on the Picard variety of the curve is stable. We introduce a homological tool for testing…

We study the stack $\mathcal{H}_{r,g,n}$ of $n$-pointed smooth cyclic covers of degree $r$ between smooth curves of genus $g$ and the projective line. We give two presentations of an open substack of $\mathcal{H}_{r,g,n}$ as a quotient…

We study the Brauer class rising from the obstruction to the existence of tautological line bundles on the Picard scheme of curves. We determine the period and index of the Brauer class in certain cases.

Dans cette note on decrit le champ des courbes hyperelliptiques lisses defines sur un corps algebriquement clos de caracteristique deux comme un champ quotient. On en deduit le groupe de Picard. ----- In this note we describe the stack…

Let S be a site. We introduce the notion of extensions of strictly commutative Picard S-stacks. We define the pull-back, the push-down, and the sum of such extensions and we compute their homological interpretation: if P and Q are two…

Three types of rigidity theorem for orbifold elliptic genus of level N are proved. The first type deals with the case where N is relatively prime to the orders of all isotropy groups. If the top exterior power of the tangent bundle is…

Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n,…

We compute the Picard group of the stack of elliptic curves equipped with a cyclic subgroup of order two, and of the stack of elliptic curves equipped with a cyclic subgroup of order three, over any base scheme on which 6 is invertible.…

We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the…

We introduce the stable module $\infty$-category for groups of type $\Phi$ as an enhancement of the stable category defined by N. Mazza and P. Symonds. For groups of type $\Phi$ which act on a tree, we show that the stable module…

We prove that the Picard group of a regular simply connected variety over an algebraically closed field of arbitrary characteristic is finitely generated. The main difficulty to overcome is the unavailability of resolution of singularities.…

We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We…