Generalizing work of Smith and Hara, we give a new characterization of logterminal singularities for finitely generated algebras over C, in terms of purity properties of ultraproducts of characteristic p Frobenii. As a first application we obtain a Boutot-type theorem for log-terminal singularities: given a pure morphism Y → X between affine Q-Gorenstein varieties of finite type over C, if Y ha...

Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs sup...

Let $f\colon Y \to X$ be a proper flat morphism of locally noetherian schemes. Then the locus in $X$ over which $f$ is smooth stable under generization. We prove that, suitable assumptions on formal fibers , same property holds for other local properties morphisms, even if only closed and flat. Our proof this statement reduces to purely question known as Grothendieck's localization problem. To ...

The harmonic morphisms φ : M → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in the case that φ is a submersion, in particular, a normal form is found for all such φ once the metric on the target manifold N is specified. The second result is a finiteness theo...

To prove that a pattern p is avoidable on a given alphabet, one has to construct an innnite language L that avoids p. Usually, L is a DOL-language (obtained by iterating a morphism h) or a HDOL-language (obtained by coding a DOL-language with another morphism g). Our purpose is to nd an algorithm to test, given a HDOL-system G, whether the language L(G) generated by this system avoids p. We rst...

Morphisms to finite semigroups can be used for recognizing omega-regular languages. The socalled strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphi...

We introduce signed exceptional sequences as factorizations of morphisms in the cluster morphism category. The objects of this category are wide subcategories of the module category of a hereditary algebra. A morphism [T ] : A → B is an equivalence class of rigid objects T in the cluster category of A so that B is the right hom-ext perpendicular category of the underlying object |T | ∈ A. Facto...