Related papers: Espaces abstraits de morphismes et mutations

In this paper we provide sufficient conditions in order to show that the set image of a continuous and shift-commuting map defined on a shift space over an arbitrary discrete alphabet is also a shift space; additionally, if such a map is…

We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we…

We provide a framework for the construction of diffeomorphism invariant sheaves of nonlinear generalized functions spaces. As an application, global algebras of generalized functions for distributions on manifolds and diffeomorphism…

We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.

We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…

We show that any extremal contraction from a smooth projective variety with dimension less than or equal to three appears as a moduli space of (semi)stable objects in the derived category of coherent sheaves.

We construct a binary mutation invariant for skew-symmetric integer matrices. The invariant is not an integer congruence invariant for matrices of odd size: we provide examples of congruent such matrices with different values for the…

In this survey article we describe moduli spaces of simple, stable, and semistable sheaves on K3 surfaces, following the work of Mukai, O'Grady, Huybrechts, Yoshioka, and others. We also describe some recent developments, including…

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the…

We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.

A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A…

Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules.…

We generalize Luna's fundamental lemma to smooth morphisms between stacks with good moduli spaces. We also give a precise condition for when it holds for non-smooth morphisms and versions for coherent sheaves and complexes. This generalizes…

Let $k$ be any field and $k^s$ its separable closure. Let $X$ be an affine variety over $k$ which is isomorphic to affine $n$-space over the field extension $k^s$. Then $X$ is isomorphic to affine $n$ space over $k$.

There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…

We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the…