Related papers: Calculations with Characteristic Cycles
Let $K$ be a finitely generated field. We construct an $n$-dimensional linear system $\mathcal{L}$ of hypersurfaces of degree $d$ in $\mathbb{P}^n$ defined over $K$ such that each member of $\mathcal{L}$ defined over $K$ is smooth, under…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
We derive a number of extremal and Ramsey stability results for cycles.
We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note.
In this paper we define and construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.
We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal…
We compute the $L$-characteristic cycle of an $A$-hypergeometric system and higher Euler-Koszul homology modules of the toric ring. We also prove upper semicontinuity results about the multiplicities in these cycles and apply our results to…
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
We compute the number of equivalence classes of nonperiodic covering cycles of given length in a non oriented connected graph. A covering cycle is a closed path that traverses each edge of the graph at least once. A special case is the…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
In this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.
An examples of solutions of the equation for curvature of congruence of cycles are constructed. Their properties are discussed.
We determine all complex hyperelliptic curves with many automorphisms and decide which of their jacobians have complex multiplication.
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective…