Related papers: Theta functions and projective structures

A set of multi-homogeneous equations for the Jacobian of a genus two curve is given. The approach used is to write down affine equations for the Jacobian minus various tranlations of the Theta-divisor by [2]-division points, and then to…

An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. The partial fraction expansion, p(s), of f(s) is obtained using the conjunction of the Riemann hypothesis and hypotheses advanced…

We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new,…

We study the theta divisor of the compactified jacobian of a nodal, possibly reducible, curve. We compute its irreducible components and give it a geometric interpretation consistent with the classical Brill-Noether theory of smooth curves.…

Let $\Theta=(\theta_{jk})_{n\times n}$ be a real skew-symmetric $n\times n$ matrix for $n\geq 2$. Under some mild non-integrality conditions on $\Theta,$ we construct Rieffel-type projections as higher dimensional Bott classes in the…

We discuss the geometry of transverse linear sections of the spinor tenfold $X$, the connected component of the orthogonal Grassmannian of 5-dimensional isotropic subspaces in a 10-dimensional vector space equipped with a non-degenerate…

This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\Theta_\omega(z)=\xi(1/2-\omega-iz)/\xi(1/2+\omega-iz)$, where $\omega>0$ is a real parameter and $\xi(s)$ is the Riemann…

The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and analytic objects. In this paper, we perform a new approach…

There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…

In this paper, we construct generalized $L$-functions associated to meromorphic modular forms of weight $\frac12$ for the theta group with a single simple pole in the fundamental domain. We then consider their behaviour towards $i\infty$…

Given a normal surface singularity $(X, Q)$ and a birational morphism to a non- singular surface $\pi : X \to S$, we investigate the local geometry of the exceptional divisor $L$ of $\pi$. We prove that the dimension of the tangent space to…

We study the birational geometry of some moduli spaces of abelian varieties with extra structure: in particular, with a symmetric theta structure and an odd theta characteristic. For a $(d_1,d_2)$-polarized abelian surface, we show how the…

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…

We extend the approach Abbott, Kedlaya and Roe to computation of the zeta function of a projective hypersurface with $\tau$ isolated ordinary double points over a finite field $\mathbb{F}_q$ given by the reduction of a homogeneous…

Suppose $Y$ is a regular covering of a graph $X$ with covering transformation group $\pi = \mathbb{Z}$. This paper gives an explicit formula for the $L^2$ zeta function of $Y$ and computes examples. When $\pi = \mathbb{Z}$, the $L^2$ zeta…

In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work math.AG/0310085 and prove that for any n>1 the map sending an abelian variety to the set of Gauss…

For every $g\geq 2$ we distinguish real period matrices of real Riemann surfaces of topological type $(g,0,0)$ from the ones of topological type $(g,k,1)$, with $k$ equal to one or two for $g$ even or odd respectively (Theorem B). To that…

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…

One can easily show that any meromorphic function on a complex closed Riemann surface can be represented as a composition of a birational map of this surface to CP^2 and a projection of the image curve from an appropriate point p in CP^2 to…

We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in ${\rm…