Related papers: Dupin cyclides passing through a fixed circle
We provide a tool to obtain local descriptions of quiddity cycles. As an application, we classify rank two affine Nichols algebras of diagonal type.
We present relations between cycles with rational coefficients modulo algebraic equivalence on the Jacobian of a curve. These relations depend on the linear systems the curve admits. They are obtained in the tautological ring, the smallest…
We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each…
In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…
We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbitrary projective morphisms. We prove several classical…
We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as…
In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…
We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded…
Using twisted nearby cycles, we define a new notion of slopes for complex holonomic D-modules. We prove a boundedness result for these slopes, study their functoriality and use them to characterize regularity. For a family of (possibly…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in…
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is…
As is well known, any complex cyclic matrix $A$ is similar to the unique companion matrix associated with the minimal polynomial of $A$. On the other hand, a cyclic matrix over a division ring $\mathbb F$ is similar to a companion matrix of…
We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…