Related papers: Reduction of divisors and Clebsch system
A theory of Clebsch-Gordan coefficients for $SL(2, C)$ is given using only rational numbers. Features include orthogonality relations, recurrence relations, and Regge's symmetry group. Results follow from elementary representation theory…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
The ``$D$'' matrices for all states of the two fundamental representations and octet are shown in the generalized Euler angle parameterization. The raising and lowering operators are given in terms of linear combinations of the left…
We show that if $X\subset\mathbb P^N_k$ is a normal variety of dimension $\geq 3$ and $H\subset\mathbb P^N_k$ a very general hypersurface of degree $d=4$ or $\geq 6$, then the restriction map $\mathrm{Cl}(X)\to\mathrm{Cl}(X\cap H)$ is an…
We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.
A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann…
We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the…
Depolarizing maps acting on an N dimensional system are completely positive maps resulting into compression of the Bloch ball along the different polarization directions. In the qubit case these maps are a convex sum of four extremal maps…
We prove relations among the classes of certain divisors on the moduli spaces of curves with marked points, generalizing the Brill-Noether Ray Theorem of Eisenbud and Harris.
By analogy with work of Hitchin on integrable systems, we construct natural relaxations of several kinds of moduli spaces of difference equations, with special attention to a particular class of difference equations on an elliptic curve…
Consider a one-parameter family of algebraic varieties degenerating to a reducible one. Our main result is a formula for the fundamental cycle of the limit subscheme of any family of effective Cartier divisors. The formula expresses this…
The classic Riesz representation theorem characterizes all linear and increasing functionals on the space $C_{c}(X)$ of continuous compactly supported functions. A geometric version of this result, which characterizes all linear increasing…
Let A be the local ring at a point of a normal complex variety with completion R. Srinivas has asked about the possible images of the induced map from Cl A to Cl R over all geometric normal domains A with fixed completion R. We use…
We investigate the automatic regularity of bounded derivations from a Banach lattice algebra of regular operators A into a Banach A-module with a Banach lattice structure compatible with the module operations.
Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to…
For Maxwell operators $(E,H) \to (i \epsilon^{-1} \nabla\times H, -i \mu^{-1} \nabla \times E)$ in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance and Leontovich boundary…
We prove an equivariant Riemann-Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in Q. We…
We study the low-lying zeros of various interesting families of elliptic curve L-functions. One application is an upper bound on the average analytic rank of the family of all elliptic curves. The upper bound obtained is less than two,…
We study ample divisors X with only rational singularities on abelian varieties that decompose into a sum of two lower dimensional subvarieties, X=V+W. For instance, we prove an optimal lower bound on the degree of the corresponding…
We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of \(3 \times 3\) matrices. Using Specht's Theorem, which characterizes when two matrices are unitarily…