Related papers: On ampleness of canonical bundle

Let $X$ be an irreducible smooth complex projective curve of genus at least two. Let $N$ be a connected component of the moduli space of semistable principal ${\rm PGL}_r({\mathbb C})$- bundles over $X$; it is a normal unirational complex…

We give a complete characterization of the holonomies of strictly convex cusps and of round cusps in convex projective geometry. We build families of generalized cusps of non-maximal rank associated to each strictly convex or round cusp. We…

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be…

We say a group is finitely annihilated if it is the set-theoretic union of all its proper normal finite index subgroups. We investigate this new property, and observe that it is independent of several other well known group properties. For…

We study the linearization of line bundles and the local structure of actions of connected linear algebraic groups, in the setting of seminormal varieties. We show that several classical results about normal varieties extend to that…

Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is…

We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 points in general position. This provides a counterexample to a conjecture of Kuznetsov and to a…

We define a notion of complexity for modules over infinite groups. We show that if $M$ is a module over the group ring $kG$, and $M$ has complexity $\leq f$ (where $f$ is some complexity function) over some set of finite index subgroups of…

Let S be a complex smooth projective surface and L be a line bundle on S. For any given collection of isolated topological or analytic singularity types, we show the number of curves in the linear system |L| with prescribed singularities is…

An account of two fundamental facts concerning finitely generated linear groups: Malcev's theorem on residual finiteness, and Selberg's lemma on virtual torsion-freeness.

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

We study the difference between internal categories and internal groupoids in terms of generalised Mal'tsev properties---the weak Mal'tsev property on the one hand, and $n$-permutability on the other. In the first part of the article we…

The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…

We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.

We survey the history of totally positive matrices and the generalization to Lie groups. We describe a reduction of a bilinear form to a canonical form (generalizing the case of symplectic nondegenerate forms) using ideas from total…

Some results that are true in classical groups are investigated in generalized groups and are shown to be either generally true in generalized groups or true in some special types of generalized groups. Also, it is shown that a Bol groupoid…

Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e.…

Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$…

Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…

We survey some recent developments on various notions of semipositivity for (1,1)-classes on complex manifolds, and discuss a number of open questions.