Related papers: Frobenius pull-back and stability of vector bundle…

In a previous paper, arXiv:1301.4409, we showed that the moduli space of curves C with a G-symmetry (that is, with a faithful action of a finite group G), having a fixed generalized homological invariant, is irreducible if the genus g' of…

Let $\pi:Y\to X$ be a surjective morphism between two irreducible, smooth complex projective varieties with ${\rm dim}Y>{\rm dim}X >0$. We consider polarizations of the form $L_c=L+c\cdot\pi^*A$ on $Y$, with $c>0$, where $L,A$ are ample…

Let $R$ be a complete discrete valuation ring with fraction field of characteristic $0$ and algebraically closed residue field of characteristic $p>0$. Let $X_R \to \mathrm{Spec}(R)$ be a smooth projective morphism of relative dimension…

Let $C$ be a nonsingular projective curve over an algebraically closed field of characteristic $p>0$ and $I\subset C$ be a finite set. If $\mathcal{U}_{C,\,\omega}$ denotes the moduli space of semistable parabolic bundles of rank $r$ and…

For a smooth projective curve $X$ over $\mathbb C_p$ and any reductive group $G$, we show that the moduli stack of $G$-Higgs bundles on $X$ is a twist of the moduli stack of v-topological $G$-bundles on $X_v$ in a canonical way. We explain…

In this article we deduce criteria for the splitting and the triviality of vector bundles, by restricting them to partially ample divisors. This allows to study the problem of splitting on the total space of fibre bundles. The statements…

Let C be a smooth projective curve with genus g>1 and Clifford index c(C) and let L be a line bundle on C generated by its global sections. The morphism i:C -->P(H^0(L))=P is well-defined and i*T is the restriction to C of the tangent…

A lot is known about the moduli space of parabolic bundles over curves of genus $g\geq 2$, but the lower genus cases are notably different. The goal of this article is to study the geometry of the moduli space of semistable parabolic…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

Some coherent sheaves on projective varieties have a non reduced versal deformation space. For example, this is the case for most unstable rank 2 vector bundles on ${\mathbb P}_2$. In particular, it may happen that some moduli spaces of…

We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex cocompact subgroups of both mapping class groups and outer…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

For every set of parabolic weights, we construct a Harder-Narasimhan stratification for the moduli stack of parabolic vector bundles on a curve. It is based on the notion of parabolic slope, introduced by Mehta and Seshadri. We also prove…

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…

The moduli stack of Deligne-Mumford stable curves of genus g admits a stratification, so that the number of nodes of the curves belonging to one stratum is constant. The irreducible components of the stratum corresponding to curves with…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a…

We give an asymptotic formula for the number of $\mathbb{F}_{q}$-rational points over a fixed determinant moduli space of stable vector bundles of rank $r$ and degree $d$ over a smooth, projective curve $X$ of genus $g \geq 2$ defined over…

We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus $1$. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We…

Let $(Z, D)$ be a pair of a smooth surface and a smooth anti-canonical divisor. Denote by $\mathfrak{M}_\beta$ the moduli stack of genus $0$ relative stable morphisms of class $\beta$ with full tangency to the boundary. Let $C_1$ and $C_2$…