Related papers: Irreducible connections admit generic oper structu…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

We prove that a degeneration rationally connected varieties over a field of characteristic zero always contains a geometrically irreducible subvariety which is rationally connected.

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable…

1-flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in differential geometry, especially in connection with the theory of affine holonomy groups.…

Take a holomorphic Lie algebroid $(V,\, \phi)$ on a compact connected Riemann surface $X$ such that the anchor map $\phi$ is not surjective. Let $P$ be a parabolic subgroup of a complex reductive affine algebraic group $G$ and $E_P\,…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…

We characterise when the log arc scheme of a fine log scheme $(X, M)$, with $X$ a variety over a field of characteristic zero, is irreducible. This generalises the theorem of Kolchin that the (ordinary) arc scheme of $X$ is irreducible…

The purpose of the present paper is to investigate $G$-opers on pointed Riemann surfaces (for a simple algebraic group $G$ of adjoint type) and their monodromy maps. In the first part, we review some general facts on $G$-opers, or more…

Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly non-connected) reductive group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In our previous work, we…

This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. Applications include new proofs that the complexes of curves, separating curves,…

We give an inductive proof that the generalized Severi varieties -- the varieties which parametrize (irreducible) plane curves of given degree and genus, with a fixed tangency profile to a given line at several general fixed points and…

Let G be an exceptional algebraic group defined over an algebraically closed field k of characteristic p>0 and let H be a subgroup of G. Then following Serre we say H is G-completely reducible or G-cr if, whenever H is contained in a…

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular. It is proved that every irreducible V^G-module occurs in an irreducible g-twisted V-module for some g in G. Moreover, the quantum…

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p. We study J.-P. Serre's notion of G-complete reducibility for subgroups of G. In particular, for a subgroup H and a normal subgroup N of H,…

We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no…

Let $\mathbf{G}$ be a connected reductive complex algebraic group with split real form $(G,\sigma)$. Consider a strict wonderful $\mathbf{G}$-variety $\bf{X}$ equipped with its $\sigma$-equivariant real structure, and let $X$ be the…

Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded…

Let $G$ be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of $G$ are uniformly admissible if and only if the irreducible smooth…