Related papers: Calculations with Characteristic Cycles
We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
For the product $X=C\times S$ of a curve and a surface over a number field, we construct unconditionally a Beilinson--Bloch type height pairing for homologically trivial algebraic cycles on $X$. Then for an embedding $f: C\to S$, we define…
In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those…
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ ring homomorphisms into an algebraic closure from an \'etale extension of…
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous…
We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.
In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures.…
We introduce augmented and restricted base loci of cycles and we study the positivity properties naturally defined by these base loci.
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
We study the family of rational curves on arbitrary smooth hypersurfaces of low degree using tools from analytic number theory.
In this series of lectures, I will discuss results for complex hypersurfaces with non-isolated singularities. In Lecture 1, I will review basic definitions and results on complex hypersurfaces, and then present classical material on the…