Related papers: Compactified Picard stacks over $\bar{\mathcal M}_…

Let $X$ be a smooth irreducible complex projective curve of genus $g\,\geq\, 2$, and let $D\,=\,x_1+\dots+x_r$ be a reduced effective divisor on $X$. Denote by $U_{\alpha}(L)$ the moduli space of stable parabolic vector bundles on $X$ of…

A cheap method for constructing canonical models and complete moduli for complex projective varieties with a structure called "rational plurifibration" is given. A result about semistable reduction (whose nature is slightly different from…

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular…

Let C be the stable oo-category of perfect complexes on a derived Deligne-Mumford stack X of finite type over the complex numbers. We prove that the complexified noncommutative topological Chern character is an isomorphism for C. In the…

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…

Let $\mathcal C$ be a smooth irreducible projective curve over the complex numbers and let $G$ be a simple simply-connected complex algebraic group. Let $\mathfrak M=\mathfrak M(G,\mathcal C)$ be the moduli space of semistable principal…

Let $G$ be a connected, simple algebraic group over an algebraically closed field. There is a partition of the wonderful compactification $\bar{G}$ of $G$ into finite many $G$-stable pieces, which were introduced by Lusztig. In this paper,…

This article treats the Picard group of the moduli (stack) of r-spin curves and its compactification. Generalized spin curves, or r-spin curves are a natural generalization of 2-spin curves (algebraic curves with a theta-characteristic),…

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the…

Let S be a site. We show that the 2-stack of strictly commutative Picard stacks over S is algebraic, i.e. it is 2-equivalent to the 2-stack of 2-algebras for an adequate algebraic 2-stack theory over S.

We determine the cycle classes of effective divisors in the compactified Hurwitz spaces of curves of genus g with a linear system of degree d that extend the Maroni divisors on the open Hurwitz space. Our approach uses Chern classes…

We study the Severi variety $V_{d,g}$ of plane curves of degree $d$ and geometric genus $g$. Corresponding to every such variety, there is a one-parameter family of genus $g$ stable curves whose numerical invariants we compute. Building on…

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

To a closed connected oriented surface $S$ of genus $g$ and a nonempty finite subset $P$ of $S$ is associated a simplicial complex (the arc complex) that plays a basic r\^ ole in understanding the mapping class group of the pair $(S,P)$. It…

We study the moduli space ${V}_4\mathcal{M}_{g}$ of Klein four covers of genus $g$ curves and its natural compactification. This requires the construction of a related space which has a choice of basis for the Klein four group. This space…

This is the first paper of a series of three. Here we give an abstract definition of the relative compactified Jacobian of a family of reduced curves. We prove that, under some mild assumptions on the family of curves, the fibres of the…

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.

Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one…

We identify the complex plane C with the open unit disc D={z:|z|<1} by the homeomorphism z --> z/(1+|z|). This leads to a compactification $\bar{C}$ of C, homeomorphic to the closed unit disc. The Euclidean metric on the closed unit disc…

We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…