Related papers: Gaussian maps on trigonal curves
There are 26 possibilities for the torsion group of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with given torsion group which give the current records for most of the torsion…
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables.…
Let X be a smooth projective curve of genus g>1 defined over an algebraically closed field k of characteristic p>0. Let M_X(r) be the moduli space of semi-stable rank r vector bundles with fixed trivial determinant. The relative Frobenius…
In this paper we present a lower bound for the domination number of the Cartesian product of a path and a cycle, that is tight if the length of the cycle is a multiple of five. This bound improves the natural lower bound obtained by using…
We study a connection between two topics: Decoding of Goppa codes arising from an algebraic curve, and rank two extensions of certain line bundles on the curve.
New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley…
We introduce manifolds with kinks, a class of manifolds with possibly singular boundary that notably contains manifolds with smooth boundary and corners. We derive the asymptotic behavior of the Graph Laplace operator with Gaussian kernel…
Let $C$ be a curve and $V \to C$ an orthogonal vector bundle of rank $r$. For $r \le 6$, the structure of $V$ can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of…
In this article we study the bicanonical map $\phi_2$ of quadruple Galois canonical covers X of surfaces of minimal degree. We show that $\phi_2$ has diverse behavior and exhibit most of the complexities that are possible for a bicanonical…
We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…
We study twisted vector bundles of infinite rank on gerbes, giving a new spin on Grothendieck's famous problem on the equality of the Brauer group and cohomological Brauer group. We show that the relaxed version of the question has an…
We present an explicit construction of tilting bundles on cotangent bundles of Grassmannians of 2-planes. This construction is based on Kapranov's exceptional collection for the underlying Grassmannians, and utilizes specific iterative…
In this note, we give a new proof of Voisin's theorem on Green's conjecture for generic curves of odd genus resembling the first two sections of "Universal Secant Bundles and Syzygies of Canonical Curves" by the author, and so avoiding the…
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection.…
We study the variation of the trace of the Frobenius endomorphism associated to a cyclic trigonal curve of genus g over a field of q elements as the curve varies in an irreducible component of the moduli space. We show that for q fixed and…
We propose a generalization of logarithmic and Schwarzenberger bundles over $\P^n=\P^n(\C)$ when the rank is greater than $n$. The first ones are associated to finite sets of points on $\P^{n\vee}$ and the second ones to curves with degree…
The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.
For $S$ a closed surface of genus $g\geq2$, we construct a canonical diffeomorphism from the degree $3$ Fock-Thomas space $\mathcal{T}^3(S)$ of higher complex structures to the $\text{SL}(3,\mathbb{R})$ Hitchin component. Our construction…
We study smooth quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$ parameterising $6 \times 6$ skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian $\mathbb{G}(1,5)$. Such surfaces correspond to…
Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally…