Related papers: The Prym-canonical Clifford index
We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a…
For each invariant polynomial $\Phi$, we construct a global CR invariant via the renormalized characteristic form of the Cheng--Yau metric on a strictly pseudoconvex domain. When the degree of $\Phi$ is 0, the invariant agrees with the…
We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic…
After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix…
This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…
In this paper we introduce the semi-graded rings, which extend graded rings and skew PBW extensions. For this new type of non-commutative rings we will discuss some basic problems of non-commutative algebraic geometry. In particular, we…
We prove that Prym varieties of algebraic curves with two smooth fixed points of involution are exactly the indecomposable principally polarized abelian varieties whose theta-functions provide explicit formulae for integrable 2D…
In this article we study graded Clifford algebras with a gradation preserving action of automorphisms given by $H_p$, the Heisenberg group of order $p^3$ with $p$ prime. After reviewing results in dimensions 3 and 4, we will determine the…
This paper is the first in a series dedicated to computing the integral Chow rings of the moduli stacks of Prym pairs. In this work, we compute the Chow ring for Prym pairs arising from a single pair of Weierstrass points and from at most…
We present a Prym analogue of Lazarsfeld's result that curves on general polarized K3 surfaces verify the Brill-Noether Theorem, or equivalently, that their canonical embedding has no unexpected secants. We show that the Prym-canonical…
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…
Principal curves are defined as parametric curves passing through the "middle" of a probability distribution in R^d. In addition to the original definition based on self-consistency, several points of view have been considered among which a…
In this paper we refine recent work due to A. Shankar, A. N. Shankar, and X. Wang on counting elliptic curves by conductor to the case of elliptic curves with a rational 2-torsion point. This family is a small family, as opposed to the…
In 2009, W. D. Banks and I. E. Shparlinski studied the average densities of primes $p \leq x$ for which the reductions of elliptic curves of small height modulo $p$ satisfy certain arithmetic properties, namely cyclicity and divisibility of…
Classical Hamming graphs are Cartesian products of complete graphs, and two vertices are adjacent if they differ in exactly one coordinate. Motivated by connections to unitary Cayley graphs, we consider a generalization where two vertices…
In this paper, we determine bundles which compute the higher Clifford indices for trigonal curves.
Let f :S\to B be a non locally trivial fibred surface. We prove a lower bound for the slope of f depending increasingly from the relative irregularity of f and the Clifford index of the general fibres.
The classical definition of Prym varieties deals with the unramified covers of curves. The aim of the present paper is to give explicit algebraic descriptions of the Prym varieties associated to ramified double covers of algebraic curves.…
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which…
Let $C \subset \mathbb{P}^3$ be a general Brill--Noether curve. A classical problem is to determine when $H^0(N_C(-2)) = 0$, which controls the quadric section of $C$. So far this problem has only been solved in characteristic zero, in…