Related papers: Complex algebraic curves. Annuli

The main goal of this paper is to give a general method to compute (via computer algebra systems) an explicit set of generators of the ideals of the projective embeddings of some ruled surfaces, namely projective line bundles over curves…

This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many clusters. This classification turns out…

We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives…

The classical Theorem of Mumford states that a topologically regular complex algebraic surface in $\mathbb{C}^3$ with an isolated singular point is smooth. We proof that any Lipschitz regular complex algebraic set is smooth. No restriction…

A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C*-algebras. We show how to build a (k+1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct…

We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…

This is a survey of some results on the structure and classification of normal analytic compactifications of C^2. Mirroring the existing literature, we especially emphasize the compactifications for which the curve at infinity is…

We address the classification problem for graph $C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that…

Given a smooth, projective curve $Y$, a point $y_0 \in Y$, a positive integer $n$, and a transitive subgroup $G$ of the symmetric group $S_{d}$ we study smooth, proper families, parameterized by algebraic varieties, of pointed degree $d$…

We introduce a general abstract notion of fine compactified Jacobian for nodal curves of arbitrary genus. We focus on genus 1 and prove combinatorial classification results for fine compactified Jacobians in the case of a single nodal curve…

We study C*-irreducibility of inclusions of reduced twisted group C*-algebras and of reduced group C*-algebras. We characterize C*-irreducibility in the case of an inclusion arising from a normal subgroup, and exhibit many new examples of…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

We provide a Hodge theoretical characterization of the set of algebraic numbers which arises from the complete list, due to A. Beauville, of semistable families of elliptic curves over $\mathbb{P}^1$ with four singular fibers. Our technical…

We classify elliptic curves over the rationals whose N\'eron model over the integers is semi-abelian, with good reduction at p=2, and whose Mordell--Weil group contains an element of order two that stays non-trivial at p=2. Furthermore, we…

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of…

We consider operators on $L^2$ spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $\mathrm C^*$-algebras that arise from suitable families of constraints, which we…

To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to…

It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…

We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…